Short Book Reviews On-Line 2000

STATISTICAL EXPERIMENTAL DESIGN AND INTERPRETATION. An Introduction with Agricultural Examples.	C.A. Collins and F.M. Seeney.
CLASSIFICATION, 2nd edition.	A.D. Gordon.
A COURSE IN CATEGORICAL DATA ANALYSIS.	T. Leonard with contributions by O. Papasouliotis.
STATISTICAL REGRESSION WITH MEASUREMENT ERROR.	C.-L. Cheng and J.W. Van Ness.
STATISTICAL MODELING BY WAVELETS.	B. Vidakovic.
INTELLIGENT DATA ANALYSIS: An Introduction.	M. Berthold and D.J. Hand (Eds.).
NONPARAMETRIC ECONOMETRICS.	A. Pagan and A. Ullah.
STATISTICAL METHODS IN SOFTWARE ENGINEERING: RELIABILITY AND RISK.	N. Singpurwalla and S. Wilson.
NEURAL NETS AND CHAOTIC CARRIERS.	P. Whittle.
FEEDFORWARD NEURAL NETWORK METHODOLOGY.	T.L. Fine.
STOCHASTIC CONTROL, HAMILTONIAN SYSTEMS AND HJB EQUATIONS.	J. Yong and X.Y. Zhou.
WHO COUNTS? The Politics of Census-Taking in Contemporary America.	M.J. Anderson and S.E. Fienberg.
POPULATION FORECASTING 1895–1945. The Transition to Modernity.	H.A. De Gans.
STATISTICAL ASPECTS OF BSE AND vCJD. Models for Epidemics.	C.A. Donnelly and N.M. Ferguson.
CHANCE RULES.	B.S. Everitt.
THE NATURE OF STATISTICAL LEARNING THEORY, 2nd edition.	V.N. Vapnik.
THE NATURE OF MATHEMATICAL MODELING.	N. Gershenfeld.
RETHINKING THE FOUNDATIONS OF STATISTICS.	J.B. Kadane, M.J. Schervish and T. Seidenfeld.
PHYSICS FROM FISHER INFORMATION: A UNIFICATION.	B.R. Frieden.
THE CONCEPT OF PROBABILITY IN STATISTICAL PHYSICS.	Y.M. Guttmann.
WAHRSCHEINLICHKEITSRECHNUNG.	D. Foata and A. Fuchs.
CHANCE ENCOUNTERS. A First Course in Data Analysis and Inference.	J. Wild and G.A.F. Seber.
SHAPE AND SHAPE THEORY.	D.G. Kendall, D. Barden, T.K. Carne and H. Le.
ANALYSIS OF HEALTH SURVEYS.	E.L. Korn and B.I. Graubard.
GROUP SEQUENTIAL METHODS WITH APPLICATIONS TO CLINICAL TRIALS.	C. Jennison and B.W. Turnbull.
MATHEMATICAL STATISTICS: A UNIFIED APPROACH.	G.R. Terrell.
MATHEMATICAL STATISTICS.	K. Knight.
BAYESIAN METHODS: An Analysis for Statisticians and Interdisciplinary Researchers.	T. Leonard and J.S.J. Hsu.
APPLIED REGRESSION INCLUDING COMPUTING AND GRAPHICS.	R.D. Cook and S. Weisberg.
REGRESSION ANALYSIS BY EXAMPLE, 3rd edition.	S. Chatterjee, A.S. Hadi and B. Price.
APPLIED MIXED MODELS IN MEDICINE.	H. Brown and R. Prescott.
LINEAR MODELS IN STATISTICS.	A.C. Rencher.
STATISTICAL MODELLING USING GENSTAT.	K.J. McConway, M.C. Jones and P.C. Taylor.
THEORY OF MULTIVARIATE STATISTICS.	M. Bilodeau and D. Brenner.
LOCAL REGRESSION AND LIKELIHOOD.	C. Loader.
SIMULATION. A Modeler's Approach.	J.R. Thompson.
LATENT VARIABLE MODELS AND FACTOR ANALYSIS, 2nd edition.	D.J. Bartholomew and M. Knott.
ELEMENTS OF SAMPLING THEORY AND METHODS.	Z. Govindarajulu.
STRATEGIES FOR QUASI-MONTE CARLO.	B.L. Fox. Norwell,
EPIDEMIOLOGY: Study Design and Data Analysis.	M. Woodward.
BIOLOGICAL SEQUENCE ANALYSIS. Probabilistic Models of Proteins and Nucleic Acids.	R. Durbin, S. Eddy, A. Krogh and G. Mitchison.
SET-INDEXED MARTINGALES.	G. Ivanoff and E. Marzbach.
SPATIAL BRANCHING PROCESSES, RANDOM SNAKES AND PARTIAL DIFFERENTIAL EQUATIONS.	J.-F. Le Gall.
PROBABILISTIC NETWORKS AND EXPERT SYSTEMS.	R. Cowell, A.P. Dawid, S.L. Lauritzen and D.J. Spiegelhalter.
UNIFORM CENTRAL LIMIT THEOREMS.	R.M. Dudley.
PRICING AND HEDGING OF DERIVATIVE SECURITIES.	L.T. Nielsen.
INTRODUCTION TO OPTION PRICING THEORY.	G. Kallianpur and R.L. Karandikar.
QUANTITATIVE MODELING OF DERIVATIVE SECURITIES.	M. Avellaneda and P. Laurence.
OPTIMAL DESIGN OF CONTROL SYSTEMS, STOCHASTIC AND DETERMINISTIC PROBLEMS.	G.E. Kolosov.
MODEL BUILDING IN MATHEMATICAL PROGRAMMING, 4th edition.	H.P. Williams.
DYNAMICAL SEARCH — APPLICATIONS OF DYNAMICAL SYSTEMS IN SEARCH AND OPTIMIZATION.	L. Pronzato, H.P. Wynn and A.A. Zhigljavsky.
ANALYSE DE RÉGRESSION APPLIQUÉE.	Y. Dodge.
QUANTITATIVE RESEARCH METHODS IN THE SOCIAL SCIENCES.	P.S. Maxim.
THE GRAMMAR OF GRAPHICS.	L. Wilkinson.
Statistics on the Table: The History of Statistical Concepts and Methods.	S.M. Stigler.
Continuous Multivariate Distributions. Volume 1: Models and Applications, 2nd edition.	S. Kotz, N. Balakrishnan and N.L. Johnson
Directional Statistics.	K.V. Mardia and P.E. Jupp.
The Theory of the design of experiments.	D.R. Cox and N. Reid.
Experiments: Planning, analysis, and parameter design optimalization.	C.F.J. Wu and M. Hamada.
The Analysis Of Variance. Fixed, Random and Mixed Models.	H. Sahai and M.I. Ageel.
Practical Strategies for experimenting.	G.K. Robinson.
Biostatistical Methods. The Assessment of Relative Risks.	J.M. Lachin.
Quantitative Investigations in the Biosciences Using Minitab™.	J. Eddison.
Reliability. Modeling, Prediction and Optimization.	W.R. Blischke and D.N.P. Murthy.
XploRe - The Interactive Statistical Computing Environment. Academic edition.	W. Härdle, S. Klinke and M. Muller.
Matrices for Statistics. 2nd edition.	M.J.R. Healy.
Symbolic Computation for Statistical Inference.	D.F. Andrews and J.E. Stafford.
Non-parametric Statistical Diagnosis.	B.E. Brodsky and B.S. Darkhovsky.
Computer-assisted Analysis of mixtures and applications. Meta-Analysis, Disease Mapping and Others.	D. Böhning.
Conditional Specification of Statistical Models.	B.C. Arnold, E. Castillo and J.M. Sarabia.
Statistical Curves and Parameters: Choosing an Appropriate Approach.	M.E. Tarter.
Decision Theory: An Introduction to Dynamic Programming and Sequential Decisions.	J. Bather.
Applications of Empirical Process Theory.	S. van de Geer.
Monte Carlo Methods in Bayesian Computation.	M.-H. Chen, Q.-M. Shao and J.G. Ibrahim.
Gaussian and non-Gaussian linear Time Series and Random Fields.	M. Rosenblatt.
Fourier Analysis of Time Series. An Introduction, 2nd edition.	P. Bloomfield.
Markov Chains, Gibbs Fields, Monte Carlo Simulation, and queues.	P. Brémaud.
Financial Derivatives in Theory and Practice.	P.J. Hunt and J.E. Kennedy.
An Introduction to Chaos in Nonequilibrium statistical mechanics.	J.R. Dorfman.
Stochastic Processes in Quantum Physics.	M. Nagasawa.
IMPLEMENTING SIX SIGMA: Smarter Solutions Using Statistical Methods.	F.W. Breyfogle III.
An introduction to support vector machines.	N. Cristianini and J. Shawe-Taylor.
Approximating Integrals via Monte Carlo and Deterministic Methods.	M. Evans and T. Swartz.
SPATIAL PATTERN ANALYSIS IN PLANT ECOLOGY.	M.R.T. Dale.
GEOSTATISTICS. Modeling Spatial Uncertainty.	J.-P. Chilès and P. Delfiner.
CLASSICAL AND SPATIAL STOCHASTIC PROCESSES	R.B. Schinazi
STATISTICAL ANALYSIS OF CATEGORICAL DATA.	C.J. Lloyd.
MODELLING AND ESTIMATION OF MEASUREMENT ERRORS.	M. Neuilly and CETAMA.
MODELS FOR REPEATED MEASUREMENTS, 2nd edition.	J.K. Lindsey.
THE ECONOMETRIC MODELLING OF FINANCIAL TIME SERIES, 2nd edition.	T.C. Mills.
PROBABILITY THEORY AND STATISTICAL INFERENCE. Econometric Modeling with Observational Data.	A. Spanos.
STATISTICAL INFERENCE. An Integrated Approach.	H.S. Migon and D. Gammerman.
SEMIMARTINGALES AND THEIR STATISTICAL INFERENCE.	B.L.S. Prakasa Rao.
STATISTICAL INFERENCE FOR DIFFUSION TYPE PROCESSES.	B.L.S. Prakasa Rao.
BOOTSTRAP METHODS: A Practitioner's Guide.	M.R. Chernick.
ESSENTIALS OF STOCHASTIC PROCESSES.	R. Durrett.
ORTHOGONAL ARRAYS. Theory and Applications.	A.S. Hedayat, N.J.A. Sloane and J. Stufken.

Contents:
1. Introduction
2. Planning
3. Design
4. Trial structure
5. Data entry and exploration
6. Analytical techniques
7. Other statistical techniques
8. Aspects of computing
APPENDIX I : Glossary of Statistical Terms
APPENDIX II : Analysis of Variance Formulae

Experimental design begins with a statement of aims, and in this book the authors guide the reader through the planning of a designed experiment. The importance of data exploration and graphical presentation are covered together with the collection and storage of data, their validation and verification. Assumptions are clearly identified but the reader is not overwhelmed with statistical theory. The statistical techniques are illustrated by the judicious use of examples based on 'real' data and an interpretation of the results is presented. Detailed formulae are given in an Appendix and mathematical equations are kept to a minimum in the main text. A section on computer packages is included but does not present a comprehensive coverage of available statistical computing facilities. The authors, not surprisingly, concentrate on the use of the two packages minitab ™ and genstat ™.
The book has been developed from a set of lecture notes used by the authors for the training of agricultural researchers, and concentrates on the design and management of arable and livestock experiments.

Contents:
1. Introduction
2. Measures of similarity and dissimilarity
3. Partitions
4. Hierarchical classifications
5. Other clustering procedures
6. Graphical representations
7. Cluster validation and description

This book provides an excellent and comprehensive overview of the classification literature. Given the progress since the first edition in 1981, it is not surprising that this edition contains a considerable amount of new material. Further, with the advent of computers and the generation of large multivariate sets of data, the book is timely; its focus is well defined. Rather than trying to include 'everything', the book concentrates on classification methods in which the number of classes or clusters as well as the characteristics of those classes are unknown and have to be determined. This is in contrast to classification methods such as those used in pattern recognition or discriminant analysis, whereby new objects are to be classified into one of a known number of classes with known characteristics. The book further concentrates on methodology based on pairwise (dis)similarity measures, and for which the 'objects' to be classified are represented by points in Euclidean space (though a brief treatment of symbolic objects is included in Chapter 5). Within the confines of these boundaries, the treatment is thorough. It is a wonderful compendium of the literature, liberally laced with the relevant references as reflected in the twenty-nine pages of references. Even where its own limits for treatment are being established, many important references for material outside those boundaries are provided.
While all chapters of this book are a pleasure to read, Chapter 7 on cluster validation tests (primarily tests with internal indices, including their limitations) and cluster descriptions sparkles. The researcher interested primarily in what to do when, is offered a wonderful roadmap. Steps to be taken are clearly delineated. In keeping with their importance, special attention is given to the assessment of partitions and of hierarchical classifications. There are lists of questions to be asked and answered. Actually, another such list of questions requiring answers in the pursuit of classification was presented in Chapter 1, which provided the backdrop on which the subsequent chapters rested. These lists together neatly frame the entire volume.
While the Preface states that the book's material has been used by honours students, in reality it can be used by statisticians and nonstatisticians alike. Indeed, anyone who has to deal with large multivariate sets of data will benefit. The writing style makes for easy and informative reading. Except for a bit of introductory level matrix algebra in Chapter 6, there is very little mathematical knowledge required on the part of the reader. This reflects the basic goal of providing a comprehensive understanding of the relevant methodologies along with a balanced appraisal of their various merits and dismerits, and on occasions an indication of where more research would be welcomed. It is necessary to go elsewhere, such as the referenced sources, to obtain proofs and justifications of these assessments and procedures. Threading their way throughout are appropriate analyses of six sets of data (also available by anonymous ftp on the web) amply illustrating the text's methodologies. In all, this volume is a valuable and welcome addition to the literature.

Contents:
Special software
1. Sampling distributions
2. Two by two contingency tables
3. Simpson's paradox and 23 tables
4. The Madison drug and alcohol abuse study
5. Goodman's full rank interaction analysis
6. Further examples and extensions
7. Conditional independence models for two-way tables
8. Logistic regression
9. Further regression models
10. Final topics

Over the past few years a number of very good texts have appeared on categorical data analysis. For the most part the emphasis of these has been on the fitting of log-linear or logistic models and examination of the fit. This book offers something different. An introduction to the binomial, Poisson, and multinomial distributions and their extensions, together with a discussion of the probability relationships between two or three variables set the mathematical basis of the book.
The author never strays far beyond the analysis of two or three dimensional contingency tables, but what a wealth of detail and insight he develops! Copious numerical examples are discussed alongside the theory, and each of these are interpreted in the context of the study that generated the data. The difference between statistical and practical significance is continually emphasized, as is the need for the statistician to develop an analysis that will enable investigators to draw meaningful conclusions from their data. The chapter on Simpson's paradox should be required reading for all budding statisticians!
In the fourth chapter, written together with Orestis Papasouliotis, the analysis of a large study on drug and alcohol abuse is described. It illustrates not only relevant statistical techniques but also the compromises that often have to be made in data analysis. Subsequent chapters show just how much information can be extracted by relatively simple analysis of two-way contingency tables. S-Plus programs for all the techniques discussed can be downloaded from the web.
All in all, while not neglecting the log-linear and logistic models, this book draws attention to aspects of the analysis of categorical data that we have perhaps tended to overlook. It is a welcome addition to the literature.

Contents:
1. Introduction to linear measurement models
2. Properties of estimates and predictors
3. Comparing model assumptions and modifying least squares
4. Alternative approaches to the measurement error model
5. Linear measurement error model with vector explanatory variables
6. Polynomial measurement error models
7. Robust estimation in measurement error models
8. Additional topics
APPENDIX A : Identification in Measurement Error Models (Overview, Structural Model, Functional Model, Identifyability and Consistent Estimation)

This volume represents a satellite expansion of Chapter 29 from The Advanced Theory of Statistics, Volume 2 (1979), pp. 399-443, authored by M.G. Kendall and A. Stuart. It is clearly written and attractively laid out, and would be excellent for a graduate seminar or as a reference book. Its strengths lie in a careful exposition of technicalities, an important achievement in this area where the literature is intricate, complex and multi-faceted. Its weaknesses lie in the presented practical application of these techniques. There are not many sets of data, and their use is somewhat perfunctory. Most of the exercises are theoretical or Monte Carlo ones. Personally, I think the geometric mean functional relationship is a useful and sensible practical technique; thus I was dismayed with the advice given on page 44!

Contents:
1. Introduction
2. Prerequisites
3. Wavelets
4. Discrete wavelet transforms
5. Some generalizations
6. Wavelet shrinkage
7. Density estimation
8. Bayesian methods in wavelets
9. Wavelets and random processes
10. Wavelet-based random variables and densities
11. Miscellaneous statistical applications

Readership: Graduate students in statistics and mathematics, practising statisticians

This book provides an excellent research resource for statisticians with an interest in wavelet methodology. If you are looking for a gentle introduction to wavelets, however, this is not the book for you; the mathematical prerequisites are high, demanding proficiency in advanced calculus and algebra. What it does provide is a useful guide to the current state of play of wavelets in statistics. Given the author's own research interests, it is not surprising to find that the coverage of wavelet shrinkage methods, and in particular Bayesian thresholding techniques, is very thorough. The coverage of other wavelet based statistical methods is more sketchy, but with enough references that the interested reader can fill in the gaps. The first five chapters are dedicated to the mathematical development of wavelets and their properties, with a slant towards the theory needed for wavelet shrinkage. Included is a chapter covering several generalizations to the basic wavelet transform, including wavelet packets and the stationary wavelet transform, such generalizations are proving important in the development of techniques for a wide range of statistical applications. The book has an associated web page:
http://www.isds.duke.edu/~brani/wiley.html containing details of the sets of data, functions and S-Plus programs referred to in the text. If this book is read alongside a more introductory wavelet text, it provides a good route for those statisticians wishing to enter the wonderful world of wavelets.

Contents:
1. Introduction
2. Statistical concepts
3. Statistical methods
4. Bayesian methods
5. Analysis of time series
6. Rule induction
7. Neural networks
8. Fuzzy logic
9. Stochastic search methods
10. Systems and applications
APPENDIX A : Tools

Intelligent Data Analysis (IDA) has been adopted as an overall term to encompass the intelligent application of data analytic tools. The complexity of real-world data requires not merely the application of statistical methods, but the complementary use of machine learning tools in order to explore and unravel hidden structure and meaning. This text provides an introductory presentation of the IDA methods currently in use, which are increasingly likely to become more important in the future. Of special note are the sections covering Bayesian belief networks and (nonlinear) dynamical systems.
This monograph contains the usual obligatory chapters covering the discussion of classical statistical issues that range from the basic concepts of probability and inference to time series methods and the Bayesian paradigm. The text does, however, contain a number of novel chapters and concludes with an overview of the IDA process. The chapters have been contributed by a number of authors but the editors have attempted to ensure that chapters complement, and build on each other. An Appendix presents a selection of IDA tools, together with postal and electronic contact addresses.

Contents:
1. Introduction
2. Methods of density estimation
3. Conditional moment estimation
4. Nonparametric estimation of derivatives
5. Semiparametric estimation of single-equation models
6. Semiparametric and nonparametric estimation of simultaneous equation models
7. Semiparametric estimation of discrete choice models
8. Semiparametric estimation of selectivity models
9. Semiparametric estimation of censored regression models
10. Retrospect and prospect
APPENDIX A : Statistical Methods

Readership: Researchers and graduate students in econometrics, non-parametric and semi-parametric statistics

Pagan and Ullah laboured for nearly a decade in "bringing together a large set of research results in semi- and nonparametric estimation" which "will be a useful resource for years to come". The quotes were gleaned from the "advanced praise" given on the back cover of the paperback edition, and sum the book up nicely. The authors of this well-produced volume merit high praise for their endeavours. This will be the most comprehensive summary of nonparametric statistics that we are likely to see for a long time. I can recommend it as a guide to recent work in an important area of mathematical statistics. The specifically econometric applications get mentioned mainly in illustrative examples.
Although destined for those beginning research, the blurb suggests its applicability for a first-year graduate course which includes logit-probit etc. This group would find it too demanding. Logit-probit is not even included in the index, getting but a passing mention in the section on the estimation of binary choice models.
The Appendix, despite being called "Statistical Methods", contains results only from probability theory, some very sophisticated indeed, with no statistics whatever if we exclude convergence results for empirical processes. Even so, as a reference for probability theorems, some quite recent, these forty pages will prove to be extremely useful.
I would have found an index of abbreviations helpful. The following are just some of the estimators referred to: GMM, MINPIN, NLR, NP2SLS.

Contents:
1. Introduction and overview
2. Foundational issues: Probability and reliability
3. Models for measuring software reliability
4. Statistical analysis and software failure data
5. Software productivity and process management
6. The optimal testing and release of software
7. Other developments: Open problems
APPENDIX A : Statistical Computations Using the Gibbs Sampler
APPENDIX B : The Maturity Questionnaire and Responses

Readership: Computer scientists, software engineers and reliability analysts, applied statisticians

This book provides a useful introduction to the range and coverage of the literature of software reliability. The book proceeds through sections on probability and reliability and introductory models for single-type software failure, to the analysis of software failure data. The application of statistical ideas within process management and to the optimal testing and release of software is also covered. In the final chapter, extensions to the previous coverage is made into open problems and newer areas including dynamic modelling and counting processes, and experimental design. Appendices are provided which demonstrate the use of the Gibbs sampler applied to some models, and the structure of a questionnaire used in the assessment of software maturity.
Overall, the book is well written and the coverage of models and analysis methods is welcomed. The extensive sections on process management and optimal testing will be very useful, particularly to practitioners. In this sense, the book will provide an audience of non-statisticians a good overview of the basic concepts and it is to be hoped encourage software engineers to apply more sophisticated statistical ideas within routine work. One slight drawback of the book is the fact that there is no coverage of multi-type failure models or data. This is a common form of failure found in practical software reliability studies and the book would have benefited by coverage of this topic also. In addition, the introduction of the Gibbs sampler as a tool of use for the intended audience may be somewhat optimistic. This aside, the book can be recommended to its intended audience as a well-written introduction to the area of software engineering.

Contents:
PART I : Opening and Themes
1. Introduction and aspiration
2. Optimal statistical procedures
3. Linear links and nonlinear knots: The basic neural net
4. Bifurcation and chaos
PART II : Associative and Storage Memories
5. What is a memory? The Hamming and Hopfield nets
6. Compound and 'spurious' traces
7. Preserving plasticity: A Bayesian approach
8. The key task: The fixing of fading data. Conclusions I
9. Performance of the probability-maximizing algorithm
10. Other memories—other considerations
PART III: Oscillatory Operation and the Biological Model
11. Neuron models and neural masses
12. Freeman oscillators—solo and in concert
13. Associative memories incorporating the Freeman oscillator
14. Olfactory comparisons. Conclusions II
15. Transmission delays
APPENDIX: Extension of the Wigner Semi-Circle Law

The brain is an enormously complex information processing system. In order to understand the mechanisms and functions of the brain and to create brain-like information processing systems, a number of prospective models of neural networks have been proposed and analyzed. Since the brain processes high-dimensional multivariate data under statistical fluctuations, statistics is one of the important tools to elucidate the brain. On the other hand, artificial neural networks provide statistics with new tractable nonlinear models, where concepts of learning and dynamics play important roles. Traditional statistics did not treat these concepts, and neural networks are now indispensable with modern statistical sciences.
There are a number of books on neural networks written from the point of view of statistics. Most of them, however, are concerned with the problem of pattern recognition and nonlinear regression by using multilayer feedforward type neural networks called the perceptron. The present book is more ambitious. The author intends to elucidate the chaotic dynamics of neural networks proposed by W. Freeman, in order to study how such dynamics are related to associative memory and pattern classification mechanisms in the brain.
The book consists of three parts. The first part explains the motivation of the book, and gives an elementary introduction to models of neural networks, and nonlinear dynamics such as bifurcation and chaos. The second part is devoted to the statistical analysis of the Hopfield net and the Hamming net. The third part begins with biological neuron models, and explains oscillatory dynamical behaviours of their networks, in particular the Freeman oscillators. The author then tries to elucidate how the chaotic neural dynamics are incorporated with associative memory functions.
The topic which the author challenges is not an easy one. Therefore, the present book cannot be said to be successful in presenting a completed theory. It rather tries to show important new ideas and directions for further studies. The book is recommended to those who search for new ambitious directions, extending the traditional framework of statistics and neural networks.

Contents:
1. Background and organization
2. Perceptrons—networks with a single node
3. Feedforward networks I: Generalities and LTU nodes
4. Feedforward networks II: Real-valued nodes
5. Algorithms for designing feedforward networks
6. Architecture selection and penalty terms
7. Generalization and learning
APPENDIX A : Note on Use as a Text

Readership: First-year graduate level readers in engineering, statistics, operations research, computer science concerned with nonlinear modelling of stochastic phenomena

Neural network theory and methods have gradually advanced over the last decade, so that now such methods are a legitimate tool in every data analyst's toolbox. They are fundamentally data driven models and have proved themselves in a wide variety of domains of applications. This book provides a formal solid statistical outline of such models. The models are set in a historical context, showing how modern forms evolved from the early perceptions. The coverage nicely integrates concepts of Vapnik-Chernovenkis dimension, growth functions, fat-shattering dimension, support vector machines in a rigorous way which is readily accessible to statisticians. The book is geared to use as a textbook, and includes exercises in an Appendix at the end. There are some constructive comments on how to use it most effectively in this role.
This is one of the nicest books on the topic I have read. It would make ideal reading for anyone contemplating undertaking research in the area.

Contents:
1. Basic stochastic calculus
2. Stochastic optimal control problems
3. Maximum principle and stochastic Hamiltonian systems
4. Dynamic programming and HJB equations
5. The relationship between the maximum principle and dynamic programming
6. Linear quadratic optimal control problems
7. Backward stochastic differential equations

Readership: Pure and applied mathematicians having an interest in stochastic optimal control problems

This is a remarkable book. The essential thrust of the book is to show the connection between the maximum principle and dynamic programming in stochastic optimal control. In doing this, it also generates results of a general nature connecting partial differential equations, stochastic differential equations and ordinary differential equations. The results have implications in many areas including control theory, mechanics, economics and mathematical finance. The book is recommended to anyone who is interested in the rigorous foundations of stochastic optimal control theory.

Contents:
1. Prologue
2. The history of the U.S. Census and the undercount
3. The undercount and the 1970 and 1980 censuses
4. Dual-system estimation and other methods for undercount
5. New for 1990: Implementing the new methods in a census context
6. Counting the population in 1990
7. Out of the limelight and into the courtroom
8. The measurement of race and ethnicity and the census undercount: A controversy that wasn't
9. Toward census 2000
10. The saga continues

Over the past few decades, the U.S. Census has been embroiled in technical, legal and constitutional, and political controversies. This book outlines how the U.S. Census has reached such a high profile. It details the history of censuses in the U.S., as well as describes in some depth the controversies associated with the 1970, 1980 and 1990 censuses and the impact on future census-taking.
As a non-American who has been following some of the developments in the U.S., I found the book gave a wonderful, clear exposition of the issues and current situation. Statisticians not familiar with these controversies will find the material both curious and fascinating. Those who have more familiarity will find that this book provides a useful summary of this complex situation.
This book combines Margo Anderson's background as a social historian and Stephen Fienberg's background in statistical methodology to create a unique narrative and commentary.

Contents:
Foreword by D.J. Van de Kaa
1. Introduction
2. A Dutch pioneer of demographic forecasting—The story of G.A.H. Wiebols (1895–1960)
3. The emergence of demographic forecasting in Europe
4. The international struggle for paradigm dominance
5. Competing methodologies in The Netherlands
6. Forecasting future housing need in The Netherlands
7. The search for practical applications in Dutch urban and regional forecasting
8. The implications of the new paradigm
9. Conclusions

Readership: Demographers, statisticians, students of the history and philosophy of social science, historians of planning

This is a story of missed international reputations on demography and statistics, woven in and out of the development of modern (i.e. cohort component-based) methods of population projection in the early 20th century, when interest was sharpened by radical demographic change. The history of these techniques starting with Edwin Cannan in 1895 is seen alongside the biographies of their neglected Dutch pioneers, the philosophical obstacles which obstructed their acceptance and the close connection of their work with the particular Dutch concern of planning. This casts a novel parochial light on a normally international subject.
The economist-statistician, G.A.H. Wiebols, is claimed to have been the first to make a cohort-survival forecast and incorporate migration into population project models. Others, for example Oly, pioneered variant projection; by the early 1930s, Dutch demographers were making projections of the populations and households of major cities, using age-specific headship rates. The Dutch language emerges as one factor in the neglect of their work, but also hostility to their methods by the more mathematically-oriented international spokesmen of Dutch statistics. I would also add the failure of Dutch planning enthusiasms to influence international intellectual fashion. Much is new here, although on a relatively small scale.

Contents:
1. Introduction
2. BSE and vCJD
3. Sources of data
4. Population models: Formulation
5. Population models: Results and sensitivity analyses
6. Individual survival models
7. Maternal risk enhancement models: Results
8. Spatio-temporal correlation and disease clustering
9. Metapopulation models
10. Prediction and scenario analysis for vCJD
11. Future directions

Readership: Statisticians, mathematical modellers, numerate biologists and medical/veterinary scientists

This book first describes the background to the BSE (bovine spongiform encephalopathy) epidemic in cattle in the United Kingdom and the almost certainly related occurrence of cases of a variant form of CJD (Creutzfeldt-Jacob disease) in the human population. The key epidemiological and demographic information available about the large number of BSE affected animals was the date of clinical onset or death of each animal and their date of birth. No information was available about the date of infection and little was known about the distribution of the incubation period. The origin of the epidemic is still subject to debate. The growth of the epidemic was driven mainly by the recycling of infected food. Little is known about the level of infectivity in material from cows at different stages of incubating the disease and the pre-clinical diagnosis of the disease is still not possible. The authors describe how their modeling of the non-linear transmission dynamics of the disease combined with the use of survival analysis, back calculation and maximum likelihood methods has, despite all these difficulties, permitted the testing of some of the alternative hypotheses about the epidemic and the robust prediction of the likely future course of the epidemic. The bringing together of realistic models of disease transmission and individual cow survival with thorough investigations of the sensitivity of the results to biological uncertainties and statistical errors in estimating the values of parameters gives this book wide relevance and interest.
The chapter on vCJD uses scenario analysis, that is stochastic sampling of the space of values for the unknown parameters, to show that the prediction of the future number of cases is too sensitive to unknown mechanisms and parameter values to be used at this stage.

Contents:
1. A brief history of chance
2. Tossing coins and having babies
3. Dice
4. Gambling for fun: Lotteries and football pools
5. "Serious gambling": Roulette, cards, and horse racing
6. Balls, birthdays, and coincidences
7. Conditional probability and the Reverend Thomas Bayes
8. Puzzling probabilities
9. Taking risks
10. Statistics, statisticians and medicine
11. Alternative therapies: Panaceas or placebos?
12. Chance, chaos, and chromosomes
Epilogue

This is a fascinating book. Not only does it discuss the topics given in the Contents in a most interesting way, but it has a wide variety of photos and drawings, including these examples: an astragalus, a detail from a Holbein painting, cricketers Bradman and Hammond, Nijinsky (the horse!), Florence Nightingale, R.A. Fisher paddling and a number of amusing cartoons. I have a couple of minor grumbles. I do not know what "[cricket] is to baseball and soccer, say, as Pink Floyd is to the Spice Girls" (p. 21) means; and the "choice" problem of p. 130 appears to be an (uncredited) revision of "The General's Dilemma", devised, according to my colleague R. Wardrop in his 1995 text Statistics: Learning in the Presence of Variation, by two psychologists called Kahneman and Tversky (see K. McKean Discover Magazine, 1985). Grumbles aside, this book would make a great present!

Contents:
Introduction: Four periods in research of the learning problem
1. Setting of the learning problem
2. Consistency of learning process
3. Bounds on the rate of convergence of learning process
4. Controlling the generalization ability of learning process
5. Methods of pattern recognition
6. Methods of function estimation
7. Direct methods in statistical learning theory
8. The vicinal risk minimization principle and the SVMs
9. Conclusion: What is important in learning theory?

The current edition is the extended version of the first one which was reviewed in Short Book Reviews, Vol. 16, p. 3. Three new chapters are mainly devoted to "support vector machines" — the techniques which are based on the kernel approximation of separating surfaces. I would like to repeat the concluding part of my review of the previous edition: "This interesting book helps a reader to understand the interconnections between various streams in the empirical modeling realm and may be recommended to any reader who feels lost in modern terminology", such as artificial intelligence, neural networks, machine learning etcetera.

Contents:
1. Introduction
2. Ordinary differential and difference equations
3. Partial differential equations
4. Variational principles
5. Random systems
6. Finite differences: Ordinary differential equations
7. Finite differences: Partial differential equations
8. Finite elements
9. Cellular automata and lattice gases
10. Function fitting
11. Transforms
12. Architectures
13. Optimization and search
14. Clustering and density estimation
15. Filtering and state estimation
16. Linear and non-linear time series
APPENDIX 1 : Graphical and Mathematical Software
APPENDIX 2 : Network Programming
APPENDIX 3 : Benchmarking
APPENDIX 4 : Problem Solutions

The book contains a wealth of basic ideas and methods of the fantastic world of mathematical modeling. These are presented in a compact and self-contained way, and are accompanied by useful algorithms and references for further reading. The book is divided into three main parts: analytical models, numerical models and observational models. Typical topics in the first part are difference and differential equations, variational calculus, ... . The second part is on numerical methods such as finite differences, finite elements, ... . The third deals with data-based modeling techniques such as curve fitting, filtering, time series, ... . Each section has a set of problems and the solutions are included at the end of the book. The book is a good introduction to the subject and will serve engineers, mathematicians, physicists, ... in their modeling work. It is a pity (but of course unavoidable) that several interesting topics have to be covered in just a few pages.

Contents:
Introduction
PART 1 : Decision Theory for Co-operative Decision Making
PART 2 : The Truth about Consequences
PART 3 : Non-co-operative Decision Making, Inference, and Learning with Shared Evidence

Readership: Philosophers concerned with decision theory, probability and statistics; statisticians, mathematicians and
economists

This book is in the Cambridge Studies in Probability, Induction and Decision Theory series. It contains sixteen previously published essays on open issues for Bayesian decision theory and statistics, with the aim being 'to understand better the scope and limitations of current Bayesian theory with the goal of contributing to its positive growth'. The book covers four principal themes: co-operative non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-co-operative, sequential decisions; and pooling rules and Bayesian dynamics for sets of probabilities.
As with any collection, the chapters differ in their depth and complexity. However, this will be of interest to anyone concerned with the foundations of probability and statistics.

Contents:
0. Introduction
1. What is Fisher information?
2. Fisher information in a vector world
3. Extreme physical information
4. Derivation of relativistic quantum mechanics
5. Classical electrodynamics
6. The Einstein field equation of general relativity
7. Classical statistical physics
8. Power spectrum 1/f noise
9. Physical constants and the 1/x law
10. Constrained-likelihood quantum measurement theory
11. Research topics
12. Summing up
APPENDIX A : Solutions common to Entropy and Fisher I-Extremization
APPENDIX B : Crámer-Rao Inequalities for Vector Data
APPENDIX C : Crámer-Rao Inequality for an Imaginary Parameter
APPENDIX D : Simplified Derivation of the Schroedinger Wave Equation
APPENDIX E : Factorization of the Klein-Gordon Information
APPENDIX F : Evaluation of Certain Integrals
APPENDIX G : Schroedinger Wave Equation as a Non-relativistic Limit
APPENDIX H : Non-uniqueness of Potential A for Finite Boundaries

Readership: Final-year undergraduates and researchers in all areas of physics; people interested in an unconventional approach to the unification of physical principles

The author aims "to develop a theory of measurement that incorporates the observer into the phenomena under measurement." Instead of Shannon or Boltzmann entropy he uses R.A. Fisher's information, I, to set up a theory of physical law which he calls the Principle of Extreme Physical Information (EPI). We read, "I is at the same time (i) a thermodynamic measure of disorder and (ii) a universal measure of information whose variation gives rise to most (perhaps all) of physics."
Statisticians may be perturbed by his treatment of certain statistical concepts, for example, when discussing the relationship of Fisher I to Kullback-Leibler entropy, and by his construction of concepts such as Fisher temperature and Fisher time. Chapter 12 gives a detailed overview of the earlier chapters. There are some interesting, unfamiliar references (with the standard form for physicists, i.e. without the title of the paper). Also, the book is illustrated with the author's drawings of John A. Wheeler, R.A. Fisher, Léon Brouin and the author. People who knew Fisher may have difficulty in recognizing him and will wonder how he would have received the book.

Contents:
Introduction
1. The neo-Laplacian approach to statistical mechanics
2. Subjectivism and the ergodic approach
3. The Haar measure
4. Measure and topology in statistical mechanics
5. Three solutions
APPENDIX I : Mathematical Preliminaries
APPENDIX II : On the Foundations of Probability
APPENDIX III : Probability in Non-equilibrium Statistical Mechanics

Readership: Philosophers of science, physicists, and mathematicians interested in foundational issues, and historians of science

This book is in the Cambridge Studies in Probability, Induction, and Decision Theory series.
What is probability, as used in statistical mechanics? Indeterminacy has no place in classical physics, in contrast to quantum mechanics, so what does it mean to make an assertion that the probability of an event A is p? The first chapter describes the early history of statistical mechanics up to the work of Gibbs, and reviews E.T. Jaynes's 'ultrasubjectivist' program, arguing that this "fails to provide a general and defensible version of statistical mechanics". The second chapter pursues the historical development after Gibbs, and then presents a more moderate subjectivist approach to statistical mechanics based on ergodic theory. The third chapter explores whether the probabilities used in statistical mechanics can be reduced to other concepts, concluding that in most cases the answer is no. The fourth chapter proposes the idea that stochastic behaviour is the result of instabilities arising from tiny differences in initial conditions — but concludes that this notion cannot replace all of the probabilistic concepts. Finally, the fifth chapter presents a new version of the subjectivist view, a new way of formulating the ergodic approach, and concludes that Gibbs 'pragmatist approach' provides a highly satisfactory solution.
The mathematical level is high, with the author arguing that attempts to reduce material of the kind presented here to a non-technical level are generally unsuccessful, at best omitting important ideas and at worst introducing errors. On the other hand, he also claims that "this book is motivated by the wish to democratize science, [to] make the connections between science and other areas of culture more evident, and make scientific ideas available to intelligent non-specialists without unduly popularizing them." I am tempted to remark that he cannot have it both ways.

Contents:
1. Die Sprache der Wahrscheinlichkeiten
2. Ereignisse
3. Wahrscheinlichkeitsräume
4. Diskrete Wahrscheinlichkeiten. Abzählungen
5. Zufallsvariable
6. Bedingte Wahrscheinlichkeit. Unabhängigkeit
7. Diskrete Zufallsvariable. Gebräuchliche Verteilungen
8. Erwartungswerte. Characteristische Werte
9. Erzeugende Funktionen
10. Stieltjes-Lebesgue-Masse. Integrale von reellen Zufallsvariablen
11. Erwartungswerte. Absolut stetige Verteilungen
12. Zufallsvektoren. Bedingte Erwartungswerte. Normalverteilung
13. Erzeugende Funktionen der Momente. Characteristische Funktionen
14. Die wichtigsten (absolut stetigen) Wahrscheinlichkeitsverteilungen
15. Verteilungen von Funktionen einer Zufallsvariablen
16. Stochastische Konvergenz
17. Gesetze der grossen Zahlen
18. Zentrale Rolle der Normalverteilung. Zentraler Grenzwertsatz
19. Gesetz von iterierten Logarithmus
20. Anwendungen der Wahrscheinlichkeitsrechnung

This book is a translation into German of the original French text Calcul des Probabilités, Cours et exercises corrigés, Masson, Paris, 1996, by the same authors. It is a good textbook for the teaching of probability theory in the second year of mathematics at university level. The first nine chapters deal with discrete probability. To make the step to non-discrete probability, some measure and integration theory is given in Chapters 10 and 11. The core of the book, Chapters 16 to 19, is on convergence, laws of large numbers, central limit theorems and laws of iterated logarithm. The book is very good for teaching a probability course on a solid basis. Each chapter has a rich choice of exercises and the solutions are worked out at the end of the book.

Contents:
1. What is statistics?
2. Tools for exploring univariate data
3. Exploratory tools for relationships
4. Probabilities and proportions
5. Discrete random variables
6. Sampling distributions of estimates
7. Confidence intervals
8. Significance testing: Using data to test hypotheses
9. Data on a continuous random variable
10. Tables of counts
11. Relationships between quantitative variables: Regression and correlation
12. Control charts (see web site)
13. Time series (see web site)

This excellent introductory text teaches what practising statisticians know but what many fail to convey to the students, namely, statistical thinking. It should be required reading for anyone embarking on a career as a statistician or in any field where critical evaluation of data is required.
The technical content is what is generally accepted as standard for an introductory statistical course: data display and summary statistics, an introduction to probability, tests on means, contingency tables, linear regression and analysis of variance. The mathematical level is pre-calculus. The subject matter is presented in a lively, informal manner without sacrificing accuracy.
The first chapter describes how statistical data can be obtained from polls and surveys, observational studies, or by experimentation and discusses the strengths and limitations of each method. The second and third chapters show how to make intelligent use of the many graphical displays and data summaries that statistical packages offer. These themes are referred to throughout the text, as the data used in the examples are evaluated. The examples themselves are interesting in their own right, being drawn from actual statistical practice, newspapers, or from learned journals in many fields. Emphasis is less on the mechanics of each procedure, bur rather on what it is for; how to interpret the result in the context of the study, and of what to be aware. Guidelines are given on important topics, such as how to proceed if outliers are present in the data: what to do if data are non-normal; the consequences of ignoring dependence between observations or collapsing contingency tables; why confidence intervals should be given together with the test results. Exercises, some of them quite challenging, follow each chapter and an instructor's manual is available.
In writing this book the authors have performed a real service to the profession. The book is highly recommended.

Contents:
1. Shapes and shape spaces
2. The global structure of shape spaces
3. Computing the homology of cell complexes
4. A chain complex for shape spaces
5. The homology groups of shape spaces
6. Geodesics in shape spaces
7. The Riemannian structure of shape spaces
8. Induced shape-measures
9. Mean shapes and the shape of the means
10. Visualizing the higher dimensional shape spaces
11. General shape spaces

Readership: Probabilists and mathematical statisticians; researchers in astronomy, archaeology, biology and other sciences modeling or interpreting shape data

During the first quarter of this century, much of the research in probability and mathematical statistics centred around the development of probability models for multidimensional data and the derivation of the associated probability distributions needed for statistical inferences based on these models. It has taken until the last quarter of the twentieth century for the shape of a multidimensional set of data to be adequately defined and a suitable mathematical framework for the analysis and application of this concept to be developed. This book provides a thorough coverage of the mathematical foundations of the theory of shape developed during the past twenty-five years by the senior author and his collaborators. The mathematical tools required for the modeling and analysis of shape are different from those usually involved in statistical models, and these may therefore present an extra challenge to some readers. The authors have, however, included considerable detail throughout, hoping thereby to make the text as widely accessible as possible.
The first seven chapters of the book are devoted to the development and analysis of shape spaces themselves. This is followed by derivations of the probability distributions on shape spaces that are induced by various Gaussian and uniform models for the underlying data. An important discussion about concepts and properties of the mean of random shapes are then presented.
This is an exemplary monograph, from an editorial as well as a scholarly perspective. It is a clearly presented unification of many years of research. The numerous figures, charts and simulation displays throughout the book represent considerable effort to clarify the material to the great benefit of the reader. The applications of shape theory that have already been made to astronomy, archaeology and biology forecast the potential value that this volume should have to researchers in many areas for years to come.

Contents:
1. Introduction
2. Basic survey methodology
3. Statistical analysis with survey data
4. Sample weights and imputation
5. Additional issues in variance estimation
6. Cross-sectional analyses
7. Analysis of longitudinal surveys
8. Analyses using multiple surveys
9. Population-based case control studies
APPENDIX A : Surveys Analyzed in this Book
APPENDIX B : Linearization for Implicit Functions of Weighted Sums
APPENDIX C : Restricted Cubic Regression Splines

The aim of this book is to describe methods for the design, implementation and analysis of large-scale health surveys, with a brief description of some of the more important surveys conducted in the U.S. today, such as the Current Population Survey, the National Health and Nutrition Examination Survey (NHANES), the National Health Discharge Survey (NHDS), and the National Health Interview Survey (NHIS). The first five chapters briefly cover estimation theory and methods for survey sampling, and include the mathematical formulae for common estimators from different survey designs. The last four chapters provide detailed analyses of different types of surveys, with specific examples taken from well-known U.S. health surveys, and are rich in tables and plots of the data. However, they do not indicate how to account for the nested structure of the surveys, which would be useful for analysts who are unfamiliar with the nesting statement constructs that are needed to estimate variances properly. Including the core SUDAAN programme statements would have been helpful. No prior knowledge of survey sampling is necessary to read the book. There are sufficient good exercises at the end of the chapters to allow use as a graduate student textbook on the subject.

Contents:
1. Introduction
2. Two-sided tests: Introduction
3. Two-sided tests: General applications
4. One-sided tests
5. Two-sided tests with early stopping under the null hypothesis
6. Equivalence tests
7. Flexible monitoring: The error spending approach
8. Analysis following a sequential test
9. Repeated confidence intervals
10. Stochastic curtailment
11. General group sequential distribution theory
12. Binary data
13. Survival data
14. Internal pilot studies: Sample size re-estimation
15. Multiple endpoints
16. Multi-armed trials
17. Adaptive treatment assignment
18. Bayesian approaches
19. Numerical computations for group sequential tests

This book represents a comprehensive presentation of group sequential methods. Written by active researchers in this area, it provides an ideal source for those wishing an introduction to the area and for those who desire a clear outline of specific topics or methods. It should quickly become a standard reference both for those wishing to apply the methods and for researchers in the area, groups which one hopes are not mutually exclusive.
The extent of coverage of various topics broadly reflects current usage. The authors have avoided undue emphasis on their own considerable contributions to the field, and the discussion of each topic appears to be well balanced. The discussion of Bayesian methods might be regarded by some as rather brief, but the references do direct the reader to the key publications on the topic.
All in all, this a very welcome book.

Contents:
1. Structural models for data
2. Least squares methods
3. Combinatorial probability
4. Other probability models
5. Discrete random variables I: The hypergeometric process
6. Discrete random variables II: The Bernoulli process
7. Random vectors and random samples
8. Maximum likelihood estimates for discrete models
9. Continuous random variables I: The gamma and beta families
10. Continuous random variables II: Expectations and the normal family
11. Continuous random vectors
12. Sampling statistics for the linear model
13. Representing distributions

This is an unusual book. It is an introductory text to Mathematical Statistics; however, it covers multiple regression, two-way layouts and logistic regression, all in the first chapter. Terrell uses a hands-on approach to the subject without compromising the mathematical details. He insists on the unity of probability and statistics, whilst still being guided by the assumption that the latter precedes the former. There are many exercises at the end of each chapter, most of them interesting. The book is very easy and enjoyable to read, though I was surprised to find no reference to resampling methods, which would fit well in the author's scheme. Nevertheless, it offers a refreshing point of view in an area which has been dominated by texts following almost exclusively by theoretical expositions.

Contents:
1. Introduction to probability
2. Random vectors and joint distributions
3. Convergence of random variables
4. Principles of point estimation
5. Likelihood-based estimation
6. Optimality in estimation
7. Interval estimation and hypothesis testing
8. Linear and generalized linear models
9. Goodness-of-fit

This book is a very suitable text for teaching statistical inference at an acceptable mathematical level with attention to the important aspects of modern statistical methodology. After a classical introduction to probability, variables, distributions and convergence, the author deals with the classical procedures for inference in (essentially) parametric models. The book contains numerous examples and each chapter is followed by a rich choice of at least twenty exercises. This makes the book excellent for teaching.

Contents:
1. Introductory statistical concepts
2. The discrete version of Bayes theorem
3. Models with a single unknown parameter
4. The expected utility hypothesis
5. Models with several unknown parameters
6. Prior structures, posterior smoothing and Bayes-Stein estimation

Readership: Graduate students in statistics, interdisciplinary research specialists with interests in a variety of areas

The text begins with an overview of "non-Bayesian" statistics at quite an advanced level. For example, in the first chapter, we find the EM algorithm, the likelihood principle and the large sample theory for likelihood procedures. From there, the authors turn to Bayesian theory. They present the basic ideas, for example prior, posterior, predictive distributions and expected utility. However, most of the book consists of significant applications, both theoretical and practical. In fact, the material develops as interplay between the latter two. Practical examples include: prediction of psychotic patients, inference for genotype frequencies, remote sensing and online quality monitoring. Theoretical examples include: non-linear regression, the Kalman filter, simultaneous estimation of normal means. Their discussion pays due regard in passing to MCMC, the Laplace approximation and important auxiliary material needed for implementing the methods. I found the "self-study" questions novel, challenging and worthwhile. Overall, this book is a very welcome and original contribution to the literature on Bayesian statistics. It will complement well more specialized books on this topic.

Contents:
PART I : Introduction
1. Looking forward and back
2. Introduction to regression
3. Introduction to smoothing
4. Bivariate distributions
5. Two-dimensional plots
PART II : Tools
6. Simple linear regression
7. Introduction to multiple linear regression
8. Three-dimensional plots
9. Weights and lack of fit
10. Understanding coefficients
11. Relating mean functions
12. Factors and interactions
13. Response transformations
14. Diagnostics I: Curvature and non-constant variance
15. Diagnostics II: Influence and outliers
16. Predictor transformations
17. Model assessment
PART III : Regression Graphics
18. Visualizing regression
19. Visualizing regression with many predictors
20. Graphical regression
PART IV: Logistic Regression and Generalized Linear Models
21. Binomial regression
22. Graphical and diagnostic methods for logistic regression
23. Generalized linear models
APPENDIX : Arc

The authors have previously written these four books:
1. Weisberg (1985), Applied Linear Regression, 2nd edition [Short Book Reviews, Vol. 1, p. 2].
2. Cook and Weisberg (1994), An Introduction to Regression Graphics [Short Book Reviews,Vol. 15, p. 23].
3. Cook and Weisberg (1982), Residuals and Influence in Regression [Short Book Reviews, Vol. 3, p. 4].
4. Cook (1998), Regression Graphics, Ideas for Studying Regressions Through Graphics.
The present volume includes: (a) "Virtually all the material in [1], ... but none of the prose," (b) "Nearly all of [2], ... little of the prose,"(c) A "low-level introduction to [3]."(d) Also, [4] "provides [the] rigorous treatment ... that is the core of the present volume."
This excellent book places an emphasis on viewing data graphically, using special software (Arc) that can be downloaded free from an Internet site. Most of the three hundred figures can thus be reproduced by the reader.

Contents:
1. Introduction
2. Simple linear regression
3. Multiple linear regression
4. Regression diagnostics: Detection of model violations
5. Qualitative variables as predictors
6. Transformation of variables
7. Weighted least squares
8. The problem of correlated errors
9. Analysis of collinear data
10. Biased estimation of regression coefficients
11. Variable selection procedures
12. Logistic regression

This third edition of Regression Analysis by Example is aimed at anyone who needs to fit equations to data to investigate underlying relationships. The approach is practical, assumes the availability of suitable model fitting statistical software, and is more concerned with the investigation and interpretation of models than with the algebra of the fitting process.
This edition is a major rewrite of earlier editions, with the material being extended by the addition of a new introduction and a complete chapter on logistic regression. More attention is given to regression diagnostics and to the use of transformations and weighted least squares. The reorganized chapters on correlated errors, collinear data and variable section procedures have been extended to include recent developments. All chapters now conclude with an exercise section.
One useful and novel feature of the book is that it has its very own website based at Cornell University. The abundance of sets of data used to illustrate the methods described in the text are all available and can be downloaded from this site. Overall, the book is very readable and effectively meets the needs of its target audience.

Contents:
Mixed Models Notation
1. Introduction
2. Normal mixed models
3. Generalised linear mixed models (GLMMs)
4. Mixed models for categorical data
5. Multi-centre trials and meta-analyses
6. Repeated measures data
7. Cross-over trials
8. Other applications of mixed models
9. Software for fitting mixed models

Readership: Applied statisticians and bio-statisticians, medical scientists, teachers and students of statistics courses

Traditionally, the techniques of analysis of variance and regression analysis have as a basic assumption that the error terms are independently and identically distributed. Mixed models are an important alternative approach to modelling which allow a relaxation of the independence assumption and accommodate more complicated data structures in a flexible way. Some benefits to be gained from using mixed models include an increase in the presence of estimates and the ability to make wider inferences.
This book has been written to provide the reader with a thorough understanding of the concepts of mixed models. The authors' intention is to put all types of mixed models into a general framework and to consider the practical implications of their use.
The SAS package has been used extensively throughout the text to analyze the majority of the examples. However, a brief review of other software available at the time of writing (MLWin, BUGS, Genstat, BMDP, MIXOR) for fitting mixed models is presented; together with details of relevant webpages where further details may be obtained.
The text is well-written, easy to read and once started, is difficult to put down.

Contents:
1. Introduction
2. Matrix algebra
3. Random vectors and matrices
4. Multivariate normal distribution
5. Distribution of quadratic forms in y
6. Simple linear regression
7. Multiple regression: Estimation
8. Multiple regression: Tests of hypotheses and confidence intervals
9. Multiple regression: Model validation and diagnostics
10. Multiple regression: Random x's
11. Analysis of variance models
12. One-way analysis of variance: Balanced case
13. Two-way analysis of variance: Balanced case
14. Analysis of variance: Unbalanced data
15. Analysis of covariance
16. Random effects models and mixed effects models
APPENDIX A : Answers and Hints to Selected Problems
APPENDIX B : Data Sets and SAS Files

The characte of this volume seems to fit roughly between Seber's Linear Regression Analysis and Hocking's Methods and Applications of Linear Models [Short Book Reviews, Vol. 17, p. 27]. The emphasis is mostly on the theory, and the author's stated objective of "clarity of exposition" has certainly been achieved. There are about four hundred and thirty-nine exercises (called "problems") of which about twenty-two (5%) offer data, taken mostly from other regression books. The one hundred and twelve pages of Appendix A supplement the theory and provide numerical details which add illustration to the examples already in the main body of the text. There is a six-page bibliography (one hundred and thirty-nine references), but no authors' index. This is a worthy addition to the Wiley regression collection.

Contents:
1. Introduction
2. Review of statistical concepts
3. Introduction to GENSTAT
4. Linear regression with one explanatory variable
5. One-way analysis of variance
6. Multiple linear regression
7. The analysis of factorial experiments
8. Experiments with blocking
9. Binary regression
10. What are generalized linear models?
11. Diagnostic checking
12. Loglinear models for contingency tables
13. Further data analysis
Postscript

This book offers an easy-to-read coverage of the uses and interpretation of basic statistical methods, covering both the general linear model (including analysis of variance and regression) and the generalized linear model. The methods are presented in the context of the software package GENSTAT 5 for Windows and the text proceeds through the analysis of seventy-eight sets of data (each accessible from the web). There are numerous exercises interspersed throughout the text with solutions at the end of the book. The topics within the book are based on the Open University's distance teaching module M346, Linear Statistical Modelling and hence, are suitable for private study.
The mathematical prerequisites for using the book are minimal (appreciation of mathematical formulae and graphs) and neither calculus nor linear algebra is required. Some familiarity with using a computer is necessary in order to gain the most benefit from the text, and some previous experience of using a statistical software package would be advantageous. Disappointingly for a book on statistical modelling, the authors neither introduce the student to computer-intensive methods nor bootstrap techniques — both of which will, without a doubt, be required once the student progresses from classroom exercises to real-world modelling applications.

Contents:
1. Linear algebra
2. Random vectors
3. Gamma, dirichlet, and F distributions
4. Invariance
5. Multivariate normal
6. Multivariate sampling
7. Wishart distributions
8. Tests on mean and variance
9. Multivariate regression
10. Principal components
11. Canonical correlations
12. Asymptotic expansions
13. Robustness
14. Bootstrap confidence regions and tests
APPENDIX A : Inversion Formulas
APPENDIX B : Multivariate Cumulants
APPENDIX C : S-Plus Functions

This is an excellent graduate level text book with several challenging problems in the exercises. An outstanding feature of this book is the presentation style. The authors' presentations of core statistical ideas, important formulae, the scope and the limitations of the topics create a curiosity to continue reading. The authors must have definitely thought through to cut down the unnecessary details to focus on the main results. The material is mathematically very rigorous. The references cite several up-to-date journal articles and other books. Unlike many other multivariate statistics books, this book offers a great exposure of robust inference in the multivariate framework. The other outstanding items include asymptotic expansions, bootstrap inference and S-Plus functions.
The minimum background needed to read this book is the knowledge gained in a sequence of mathematical statistics courses. For the sake of readers who are unfamiliar with linear algebra, the authors have presented all the necessary material in Chapter 1 itself. This can be used as a text book for a one-semester theoretical graduate course. This is not suitable for an applied multivariate statistics course. There is no statistical table, for example.
However, the researchers and graduate students who wish to publish in journals will undoubtedly gain a lot of knowledge and insight of the core multivariate statistical ideas and techniques by reading this well-written book. I enjoyed reading this book and learned a lot!

Contents:
1. The origins of local regression
2. Local regression methods
3. Fitting with LOCFIT
4. Local likelihood estimation
5. Density estimation
6. Flexible local regression
7. Survival and failure time analysis
8. Discrimination and classification
9. Variance estimation and goodness-of-fit
10. Bandwidth selection
11. Adaptive parameter choice
12. Computational methods
13. Optimizing local regression
APPENDIX A : Installing LOCFIT in R, S and S-Plus
APPENDIX B : Additional Features: LOCFIT in S
APPENDIX C : C-LOCFIT
APPENDIX D : Plots from C-LOCFIT

Readership: Research and applied statisticians, graduate students in statistics, others interested in nonparametric regression techniques

This book is another well-written monograph in the popular area of data smoothing and local nonparametric estimation. The emphasis of the monograph is on both the methodology and applications from a wide range of fields. The author covers traditional aspects of local smoothing (bias-variance balance, bandwidth choice, confidence bounds) as well as topics which are not often discussed in the textbooks on nonparametric regression (for example, survival analysis and estimation of hazard rates). Numerous examples in the book are analyzed with LOCFIT, a software package which may be run within an S, R or S-Plus environment, or as a stand-alone application, and which is available through the World Wide Web from the author's homepage.

Contents:
1. The generation of random numbers
2. Random quadrature
3. Monte Carlo solutions of differential equations
4. Markov chains, Poisson processes, and linear equations
5. SIMEST, SIMDAT and pseudoreality
6. Models for stocks and derivatives
7. Simulation assessment of multivariate and robust procedures in statistical process control
8. Noise and chaos
9. Bayesian approaches
10. Resampling-based tests
11. Optimization and estimation in a noisy world
12. Modelling the AIDS epidemic: Exploration, simulation, and conjecture

The reader is drawn into the book immediately via the Preface, where the well-known three-door quiz show problem is discussed and illuminated by a small simulation program. The discussion is attractively plain and straightforward throughout the book, and is illustrated by many diagrams. This is a very readable and user-friendly book, and is highly recommended. (I note, in passing, a couple of typographical errors on p. 110, two lines from the bottom, and p. 267, four lines from the bottom.)

Contents:
1. Basic ideas and examples
2. The general linear latent variable model
3. The normal linear factor model
4. Binary data: Latent trait models
5. Polytomous data: Latent trait models
6. Latent class models
7. Models and methods for manifest variables of mixed type
8. Relationships between latent variables

This is a completely reworked version of the book of the same title originally published by the first author in 1987 in Griffin's Statistical Monograph Series. Existing material has been updated, the structure has been revised, and three chapters of new material have been added: Chapter 2 presents a general framework which includes subsequent models as special cases and which links these models to the generalized linear model of statistics; Chapter 7 gives recent methods for mixed types of variables; and Chapter 8 covers confirmatory factor analysis and linear structural relationships.
The outcome is a very elegant and original treatment of latent variable models, which brings a relatively unfamiliar topic firmly into the mainstream of statistical theory. While much of the material is necessarily terse, the coverage is comprehensive and up-to-date. Sufficient references enable the interested reader to follow up on detail, and about one third of the over two hundred and seventy references cites work published in the last decade. There are plenty of numerical examples, and access is provided to specialized software via the Arnold website. This book should appeal to newcomer and old hand alike.

Contents:
1. Preliminaries
2. Varying-probability sampling
3. Simple random sampling
4. Estimation of the sample size
5. Stratified sampling
6. Ratio estimators
7. Regression estimators
8. Systematic sampling
9. Cluster sampling
10. Varying-probability sampling: Without replacement
11. Two-phase and repetitive sampling
12. Two-stage sampling
13. Non-sampling errors
14. Bayesian approach for inference in finite populations
15. The jackknife method
16. The bootstrap method
17. Small-area estimation
18. Imputations in surveys

This text covers an extensive amount of material from the simplest of sampling designs to modern computationally intensive methods using the jackknife and bootstrap procedures. The claim is that the book is suitable for a one-semester graduate level course; but this is ambitious, unless the students are expected to read much of the detail in their own time. The book covers all the usual concepts of design and estimation methods and includes many proofs of the main results. In addition, new material on the Bayesian approach, the jackknife and bootstrap methods are included as well as chapters on small area estimation and modern imputation methods. Each chapter contains illustrative numerical examples and concludes with a problem section for which answers are provided at the end of the book.
The approach is very much based on theorems, lemmas, proofs and corollaries, with extensive reference to well-known and recently published research. This leads to a well-structured and logical development of most, if not all of the results that a sample survey researcher or practitioner would wish to know. Also included is a comprehensive list of approaching two hundred references, many of which appeared in the late 80's or early 90's. The text could be used either as a course text, requiring basic algebra and statistical inference, or as an initial reference source.

Contents:
1. Introduction
2. Smoothing
3. Generating Poisson processes
4. Permuting order statistics
5. Generating Bernoulli trials
6. Generating Gaussian processes
7. Smoothing summation
8. Smoothing variate generation
9. Analysis of variance
10. Bernoulli trials: Examples
11. Poisson processes: Auxiliary matter
12. Background on deterministic QMC
13. Optimization
14. Background on randomized QMC
15. Pseudocodes

Readership: Applied mathematicians and operations researchers with some experience with Monte Carlo or quasi-Monte Carlo

This book presents in an erudite but informal style a broad picture of the author's ideas on the topic of randomized quasi-Monte Carlo. By carefully distinguishing a small number of important variables, and other less important variables, the methods (presented in the form of pseudocode) proposed in this book allow beating the curse of dimensionality in many applications. Variance decomposition and quantification is emphasized throughout. Each problem can be attacked by a combination of techniques varying from Latin hyper- (or super-) cubes, via stratification, importance sampling, Russian roulette, to naive Monte Carlo. Examples from queueing, finance and optimization illustrate the ideas.

Contents:
1. Fundamental issues
2. Basic analytical procedures
3. Assessing risk factors
4. Confounding and interaction
5. Cohort studies
6. Case-control studies
7. Intervention studies
8. Sample size determination
9. Modelling quantitative outcome variables
10. Modelling binary outcome data
11. Modelling follow-up data
APPENDIX A : SAS Programs
APPENDIX B : Statistical Tables
APPENDIX C : Example Data Sets

It is evident that the author knows his subject well. Much of the material is taken from his course notes. The volume consists of two quite disjoint and uneven parts. Chapters 1 to 8 introduce nicely in three hundred and sixty-five pages the basic concepts of epidemiology, the different designs together with their merits, and the classical methods of analysis. The chosen approach, named practical, and the idea that understanding is closely linked to being able to perform the analysis seems to work well in this part of the book.
The remaining three chapters seem to be an extra addition to this assemblage. These chapters give examples of models but do not introduce the idea of generalized linear models. The heterogeneity of the intended readership makes the introduction of generalized linear models difficult; perhaps so difficult that it was wise not even to try. The heavy dependency on computer programs make these examples of models cumbersome. Here, understanding does not go together with ability to perform the analyses; the commands of computer packages are not designed to clarify the problem for humans but for the machine. The theoretical origin of the models is not used for the motivation nor for the clarification.
The origin of the work, material taken from course notes, might explain the major difficulty of the book, the division into two disjoint parts. If the concept of modelling is considered an essential part of epidemiological data analysis, the models presented at the end of the book should have been introduced already when the related tests were brought to the use in their proper epidemiological context. The examples given prove that this would have been possible.

Contents:
1. Introduction
2. Pairwise alignment
3. Markov chains and hidden Markov models
4. Pairwise alignment using HMMs
5. Profile HMMs for sequence families
6. Multiple sequence alignment methods
7. Building phylogenetic trees
8. Probabilistic approaches to phylogeny
9. Transformational grammars
10. RNA structure analysis
11. Background on probability

In biological sequence analysis, one attempts to infer structural and functional similarity and/or common evolutionary origin of genes and proteins by comparing their linear codes—the four-letter DNA alphabet for genes or the twenty-letter amino acid alphabet for proteins. The simplest problem involves the alignment of two words according to a scoring system that rewards similarities of aligned letters and penalizes "gaps", which one is allowed to insert in either word to increase the score of the aligned letters. The problems are computational—determining the optimal alignment for the chosen reward scheme—and evaluative—assessing the statistical and/or biological significance of a near optimal alignment. More complex problems, where formulations as well as proposed solutions proliferate, involve the alignment of multiple sequences and the application of multiple alignments to study phylogenetic relationships (which in practice often proceed from a given multiple alignment and ignore the variability implicit in the aligning process).
Biological Sequence Analysis provides a broad overview of alignment methods and applications, largely from an algorithmic point of view. Chapter 2 gives a broad survey of the now reasonably standard problem of pairwise alignments from the dynamic programming (Smith-Waterman) and heuristic (e.g., BLAST) viewpoints. Starting with Chapter 3, the book focuses on the authors' main interest: hidden Markov models implemented by the Baum-Welch/EM algorithm. Chapter 3 discusses hidden Markov models for analysis of single sequences, with judicious simple applications to an "occasionally dishonest casino" and to the biological problem of identifying CpG islands. Pairwise alignments using hidden Markov models and their relationship to alignments obtained by dynamic programming are the subject of Chapter 4. Chapters 5–10 are concerned with the more ambitious and less settled problems of multiple alignments and their applications, particularly to phylogenetics. Chapter 11 gives a helpful review/introduction of statistical ideas used throughout the book.
The book provides a particularly lucid discussion of the conceptual framework of sequence analysis—what does one want to accomplish and why. The technical exposition stresses broadly useful ideas and avoids detailed discussion of implementation. Many references and helpful comments about the references complete the pathway that will allow the novice to catch up with the experts, should the problems seem appealing. Overall, the book presents the reader with an enjoyable opportunity to see a blend of modeling and data analysis at work on an important class of problems in the rapidly growing field of computational biology.

Contents:
Introduction
1. Generalities
2. Predictability
3. Martingales
4. Decompositions and quadratic variation
5. Martingale characterizations
6. Generalizations of martingales
7. Weak convergence of set-indexed processes
8. Limit theorems for point processes
9. Martingale central limit theorem

In a small, elegant volume, the idea of set-indexed stochastic process is combined with the theory of martingales. Motivations come from spatial statistics and stochastic geometry. This "foretaste of the subject" is based mostly on a series of papers by the authors and their co-authors. Finding the "right" definitions is paramount. Among the results are stopping theorems, extensions of Doob-Meyer decomposition, existence of quadratic variation, versions of localization and of weak convergence, and finally set-indexed martingale central limit theorems. The considerable bibliography includes key works on stochastic geometry, multiparameter processes, random fields, and related topics, as well as set-indexed martingales. This state-of-the-art monograph will be a valuable resource and stimulus for further work in the area.

Contents:
1. An overview
2. Continuous-state branching processes and superprocesses
3. The genealogy of Brownian excursions
4. The Brownian snake and quadratic superprocesses
5. Exit measures and the non-linear dirichlet problem
6. Polar sets and solutions with boundary blow-up
7. The probabilistic representation of positive solutions
8. Lévy processes and the genealogy of general continuous-state branching processes

Most readers of this review will be familiar with the Galton-Watson (G-W) branching process as a simple Markov chain (the sequence of generation sizes) describing the evolution of the size of a population in discrete-time. This process has the obvious additive property that the sum of two independent G-W processes with the same offspring distribution is again a G-W process. Additional information is provided by the genealogy (tree structure) of the process, and a spatial version is obtained if each population member has an initial position at birth, and is allowed to move (independently, and with a common distribution) between successive time points.
The additive property mentioned above is the basis for a generalization to branching processes having continuous states and in which the branching occurs in continuous time. Such spatial processes, or superprocesses, can be viewed as limits of suitably rescaled discrete-time processes, and form the subject of this monograph. Different branching mechanisms and movement distributions give rise to important special cases and links with other stochastic processes.
This is a research monograph, and the mathematical theory described is non-trivial. Nevertheless, the exposition is exceptionally clear and well-structured, with careful attention to motivation and explanation. The prerequisites are a basic familiarity with the theory of stochastic processes and Brownian motion. There is a useful set of notes giving the bibliographic history of this subject, which is a recent one — the great majority of the references are to work published in the last ten years.

Contents:
1. Introduction
2. Logic, uncertainty, and probability
3. Building and using probabilistic networks
4. Graph theory
5. Markov properties on graphs
6. Discrete networks
7. Gaussian and mixed discrete-Gaussian networks
8. Discrete multistage decision networks
9. Learning about probabilities
10. Checking models against data
11. Structural learning
Epilogue
APPENDIX A : Conjugate Analysis for Discrete Data
APPENDIX B : Information and Software on the WWW

Readership: Researchers interested in expert systems and familiar with basics of probability theory and statistics

The main topic of the book is probabilistic modeling of expert systems. The authors cover the huge array of related topics starting from various interpretations of the concept of probability and Kolmogorov's axioms and wandering through machine learning, neural networks, artificial intelligence, hidden Markov chains, EM algorithms, Gibbs sampling, Bayesian conjugate analysis, hyper Markov laws, etc. Frequently, the depth of discussion and reasoning is replaced by an extensive referencing which results in thirty pages of bibliography and author index.

Contents:
1. Introduction: Donsker's theorem, metric entropy, and inequalities
2. Gaussian measures and processes, sample continuity
3. Foundations of uniform central limit theorems: Donsker classes
4. Vapnik-Èervonenkis combinatories
5. Measurability
6. Limit theorems for Vapnik-Èervonenkis and related classes
7. Metric entropy, with inclusion and bracketing
8. Approximation of functions and sets
9. Sums in general Banach spaces and invariance principles
10. Universal and uniform central limit theorems
11. The two-sample case, the bootstrap and confidence sets
12. Classes of sets or functions too large for central limit theorems

The book gives an exposition on the central limit theory for independent and identically distributed random variables in its full generality: the convergence of the empirical process, uniformly over large classes of functions. The book grew out of the author's 1984 St.-Flour lecture notes but it is also updated with some results and references from the nineties. The book is very mathematical and the proofs are carefully worked out. Each of the twelve chapters ends with a list of interesting notes, a set of exercises and a bibliography. It is for certain that this will soon be a classic piece of work in the empirical process literature.

Contents:
Introduction
1. Stochastic processes
2. Itô calculus
3. Gaussian processes
4. Securities and trading strategies
5. The martingale valuation principle
6. The Black-Scholes model
7. Gaussian term structure models
APPENDIX A : Measure and Probability
APPENDIX B : Lebesgue Integrals and Expectations
APPENDIX C : The Heat Equation

Readership: More quantitative oriented students and researchers interested in modern, mathematical finance

This interesting text gives a very readable introduction to the mathematics of derivative pricing and hedging. The mathematical level is high, despite the fact that the author works in practice. The latter practical background clearly shows itself through the various pedagogical discourses, either through examples or discussions on ramifications of the methodology presented.
I found the author's style of writing close to perfect: the material presented would make an excellent course. Mathematicians will get a lot out of the book because of the extra practical insight, but also because the author has taken great care to explain the sophisticated mathematics in a very clear and concise way. The more applied reader may find this text a possible step to get on the high level of mathematical sophistication present (partly needed) in modern finance. In order to help this category of potential readers, about eighty pages of mathematical background material (including measure theory) is included. This makes the text close to self-contained.
I personally would have liked more material on the core subject; there are numerous excellent and very readable texts out there, catering for the mathematical background. All in all, I highly recommend this text to those prepared to invest the necessary time and effort for learning the subject of derivatives. It will no doubt become one of my favourites.

Contents:
1. Stochastic integration
2. Itô's formula and its applications
3. Representation of square integrable martingales
4. Stochastic differential equations
5. Girsanov's theorem
6. Option pricing in discrete time
7. Introduction to continuous time trading
8. Arbitrage and equivalent martingale measures
9. Complete markets
10. Black and Scholes theory
11. Discrete approximations
12. The American options
13. Asset pricing with stochastic volatility
14. The Russian options

Readership: Students and researchers in probability, statistics, applied mathematics, business or economics, who have a
background in measure theory and have completed probability theory at the intermediate level

There are now many books on option pricing and the financial markets. They range from the relatively simple, perhaps aimed more at the management school end of the market, to the more mathematically demanding, using measure theoretic notions, stochastic integration, and so on. This book is clearly at the latter end of the continuum, with the first five chapters being devoted to the mathematical background, before the notions of options, arbitrage, and so on are introduced in Chapter 6. Some of the later chapters present new results.
This book would be suitable for mathematics graduates (the Preface says the book is intended for probabilists) who want a solid introduction to the underlying mathematics of option pricing. It is presented in the theorem-proof style. It does not include any exercises.

Contents:
Introduction
1. Arbitrage pricing theory: The one-period model
2. The binomial option pricing model
3. Analysis of the Black-Scholes formula
4. Refinements of the binomial model
5. American-style options, early exercise, and time-optionality
6. Trinomial model and finite difference schemes
7. Brownian motion and Itô calculus
8. Introduction to exotic options: Digital and barrier options
9. Itô processes, continuous-time martingales, and Girsanov's theorem
10. Continuous-time finance: An introduction
11. Valuation of derivative securities
12. Fixed-income securities and the term-structure of interest rates
13. The Heath-Jarrow-Morton theorem and multidimensional term-structure models
14. Exponential-affine models
15. Interest-rate options

Readership: Theoreticians, practitioners and postgraduate students of mathematical finance

This is a textbook, though it contains no exercises, on the theory underlying the modeling and risk management of financial derivatives. The authors attempt to link theory with practice, not flinching from pointing out that the theory does not have all the answers. The mathematical style is informal, assuming an understanding of linear algebra and elementary probability, but not requiring a grasp of measure theory. It introduces stochastic calculus. Some background financial knowledge would be helpful. Essentially, the book is divided into two halves, with Chapters 1 to 8 dealing with discrete lattice models and Chapters 9 to 15 with continuous time models.
Despite the recent publicity concerning how physics PhDs can find highly remunerative employment in this area, the authors point out that "financial modeling is very different from modeling in the natural sciences. Unlike physics, where we deal with reproducible experiments with well-defined initial conditions, the models and ideas presented in this book deal with phenomena for which we have only limited information and that are not necessarily reproducible." To me this seems to pose a challenge perfectly matched to statistical techniques. Overall, it would be worth considering as a text for a postgraduate course on arbitrage pricing theory.

Contents:
1. Synthesis problems for control systems and the dynamic programming approach
2. Exact methods for synthesis problems
3. Approximate synthesis of stochastic control systems with small control actions
4. Synthesis of quasioptimal systems in the case of small diffusion terms in the Bellman equation
5. Control of oscillatory systems
6. Some special applications of asymptotic synthesis methods
7. Numerical synthesis methods
Conclusion

This book studies classes of deterministic and stochastic optimal control problems. The former leads to open-loop solutions whilst the latter depends on feedback solutions. The principal tool used to study these problems is the Dynamic Programming method due to Bellman. Emphasis is placed on approximate synthesis methods leading to finite analytic solutions or, at least, solutions which are simple to implement. The book goes beyond linear quadratic problems (whose solution is well-known) to more general problems, for example, those constraints or those where model parameters are unknown (adaptive control). The book would be interesting to readers seeking insight into dynamic stochastic optimization problems.

Contents:
1. Introduction
2. Solving mathematical programming models
3. Building linear programming models
4. Structured linear programming models
5. Applications and special types of mathematical programming models
6. Interpreting and using the solution of a linear programming model
7. Non-linear models
8. Integer programming
9. Building integer programming models I
10. Building integer programming models II
11. The implementation of a mathematical programming system of planning
12. The problems
13. Formulation and discussions of problems
14. Solutions to problems

This unique book, now in a fourth revised edition, should be on the shelves, having been read of course by everyone, whether practitioner or teacher, with any interest in mathematical programming. It is devoted entirely to mathematical programming models: linear, non-linear, integer and stochastic. There is no description of any algorithm. The book is in two sections. The first section, Chapters 1 to 11, discusses the use of the different models and, importantly, their management and maintenance. The second section, Chapters 12 to 14, about a third of the text, describes,
formulates and gives the solution of twenty-four problems. The level of mathematics needed is minimal; the author carefully explains in words before giving an algebraic formulation. Read and use this text; you will enjoy it as I have done since the first edition.

Contents:
1. Introduction
2. Consistency
3. Renormalization
4. Rates of convergence
5. Line-search algorithms
6. Ellipsoidal algorithms
7. Steepest-descent algorithms
8. Appendices

Readership: Mathematicians, engineers or statisticians with an interest in optimization

This is a fascinating book which links optimization algorithms with the properties of certain dynamical systems. This link allows one to better understand the optimization algorithms and to ultimately construct more efficient versions of them. Optimization lies at the core of many problems in economics, statistics, engineering and mathematics. Hence, this book should be of interest to a wide audience.

Table des matières:
1. Analyse de régression linéaire
2. Régression linéaire simple
3. Régression multiple
4. Corrélation
5. Diagnostics
6. Choix du modèle
7. Analyse de variance et régression
8. Régression ridge
9. Régression LAD
10. Conclusion

Ce livre consacré à l'analyse de la régression sera très utile pour l'enseignement en langue française, parce que les ouvrages sur ce sujet dans cette langue ne sont pas très nombreux. A peu près la moitié du livre est une présentation pédagogique sur la régression simple et multiple. Après on discute la vérification des hypothèses du modèle, la sélection des variables, l'analyse de variance et quelques méthodes alternatives à celle des moindres carrés.
Ce livre est très intéressant pour utiliser comme manuel, surtout grâce aux examples et aux exercises avec solutions.

Contents:
1. The scientific method
2. Theory formalization
3. Causality
4. Statistical inference
5. Sampling: Basic statistics
6. Sampling: Design
7. Sampling: Special problems
8. Experimental designs
9. Measurement theory
10. Classical test theory
11. Confirmatory factor models
12. Data collection methods and measurement errors
13. Missing data
14. Interpolating and smoothing
15. Computer-intensive hypothesis testing

The main objectives of this book are to provide a discussion of methods that can build upon a student's undergraduate study and provide an overview of how the various issues and techniques employed in the social sciences interrelate. The topics covered in this book range from the philosophical basis of scientific research to issues involving classical statistics. The author demonstrates the technique with a wealth of practical examples drawn from a variety of applications. The various utilities and disadvantages of the methods used are elucidated in great depth. A comprehensive reference list is included so that the reader can follow up various techniques and discussion topics in greater detail if required. However, the book is a very comprehensive text, and I doubt if the reader will need to follow up the references included. A useful reference text for students and researchers in the social science field of statistics.

Contents:
1. Introduction
2. How to make a pie
3. Data
4. Variables
5. Algebra
6. Geometry
7. Aesthetics
8. Statistics
9. Scales
10. Coordinates
11. Facets
12. Guides
13. Graphboard
14. Reader
15. Semantics

Readership: Students of computer science and statistics; mathematicians, statisticians and computer scientists; specialists in computer graphics

The work of Leland Wilkinson became known to many statisticians and users of statistics through the computer package SYSTAT and its graphical adjunct SYGRAPH. This book reveals the kind of thinking that produced the versatile graphics component of those packages, and offers a foundation for quantitative graphics in the distributed computing environments of the future.
In the Grammar of Graphics, the difficult and subtle task of visually representing statistical data is described systematically in terms of "parts of speech" and "grammatical rules" for combining them into coherent visual statements. This natural paradigm readily lends itself to an object-oriented approach to designing graphics systems which, in turn, leads to efficient and powerful programming in a language such as, for example, Java.
Chapter 2 introduces many of the main concepts by working through an old favourite example, the ubiquitous pie chart. Thereafter, the several attributes of graphics are studied in detail, the chapter titles giving a hint of the content. Chapters 5 through 8, comprising over a third of the book, present the main components for assembling a graphic and contain a large collection of examples. There are valuable insights on interpreting data and comments on other methodologies including a pithy critique of data mining.
Online files are promised, but have so far remained elusive.

Contents:
Introduction
Part I: Statistics and Social Science
1. Karl Pearson and the Cambridge economists
2. The average man is 168 years old
3. Jevons as statistician
4. Jevons on the King-Davenant law of demand
5. Francis Ysidro Edgeworth, statistician
Part II: Galtonian Ideas
6. Galton and identification by fingerprints
7. Stochastic simulation in the nineteenth century
8. The history of statistics
9. Regression towards the mean
10. Statistical concepts in psychology
Part III: Some Seventeenth-Century Explorers
11. Apollo mathematics
12. The Dark Ages of probability
13. John Graig and the probability of history
Part IV: Questions of Discovery
14. Stigler's law of eponimy
15. Who discovered Bayes' theorem
16. Daniel Bernoulli, Leonhard Euler, and maximum likelihood
17. Gauss and the invention of least squares
18. Cauchy and the witch of Agnesi
19. Karl Pearson and degrees of freedom
Part V: Questions of Standards
20. Statistics and standards
21. The trail of the Pyx
22. Normative terminology (with W.H. Kruskal)

Readership: Anyone with a serious interest in statistics, who desires to be instructed, stimulated and amused

The list of chapter headings indicates the very wide range of topics. But this most remarkable collection of essays will still surprise even those who have read many of the original versions and are acquainted with the author's breadth of erudition and lively and witty style. Statistical theory and practice have for centuries entered into most aspects of living; but this reviewer remains astonished at the extent and the depth of the further coverage now presented.
The title is taken from Karl Pearson's controversy with the Cambridge economists, Marshall, Keynes and Pigou who in the second decade of the past century were confidently asserting that "drink" was responsible for much of the poverty then widespread in advanced countries. Pearson and his assistant Ethel M. Elderton had collected statistical evidence to the contrary, and having presented this, Pearson requested – in vain – that the three pundits should put their evidence "on the table".
The renaming and discussion of the "aggregation paradox" is a most important clarification of what has so often been misascribed to Simpson. And those who recall Stigler's discussion of the many alternative candidates for the credit of having discovered Bayes' Theorem will note the concrete evidence he now presents in support of the proposition that it just possibly might have been Lady Diana Spencer.

Contents:
1. Systems of continuous multivariate distributions
2. Multivariate normal distributions
3. Bivariate and trivariate normal distributions
4. Multivariate exponential distributions
5. Multivariate gamma distributions
6. Dirichlet and inverted Dirichlet distributions
7. Multivariate Liouville distributions
8. Multivariate logistic distributions
9. Multivariate Pareto distributions
10. Bivariate and multivariate extreme value distributions
11. Natural exponential families

Readership: Pure and applied statisticians, researchers and graduate students in distribution theory, scientists who use distributions

This second edition is more than twice the length of its nine-chapter original (the last of the four-volume Distributions in Statistics by Johnson and Kotz), first published in 1972. It reflects activity and changes in the direction and scope of research during the last quarter of the century. Each of the first three chapters (which together occupy half the book) contain nearly all the material in the corresponding chapter of the original, plus at least as much new update material. From thereon, the revision is more drastic. The original three chapters on multivariate-t, Wishart, and other sampling distributions associated with the multivariate normal distribution have been completely omitted. There is, however, very substantially expanded and updated coverage of various topics from the remaining three original chapters (which were on multivariate beta and gamma distributions, multivariate extreme value and exponential distributions, and miscellaneous real multivariate distributions). Virtually all the work reported in the new chapter on the multivariate Liouville distributions was carried out during the past quarter-century. The same is true of the entirely new concluding chapter (contributed by Professor Muriel Casalis) on natural exponential families. Each chapter of the book ends with its own comprehensive bibliography which, for completeness, contains some items not specifically referred to in the text. This book brings one right up to date and is a worthy addition to the existing set of second editions of the other volumes of Distributions in Statistics. It will remain the key reference for many years.

Contents
1. Circular data
2. Summary statistics
3. Basic concepts and models
4. Fundamental theorems and distribution theory
5. Point estimation
6. Tests of uniformity and tests of goodness-of-fit
7. Tests on von Mises distributions
8. Non-parametric methods
9. Distributions on spheres
10. Inference on spheres
11. Correlation and regression
12. Modern methodology
13. General sample spaces
14. Shape analysis
Appendix 1: Special Functions
Appendix 2: Tables and Charts for the Circular Case
Appendix 3: Tables for the Spherical Case
Appendix 4: List of Notation

This book has been written as a drastic revision and major extension to Statistics of Directional Data (Mardia, 1972). It is a worthy successor to that book and will surely become the definitive reference on this subject area for many years. The book has three parts. The first part (Chapters 1-8) is concerned with statistics on the circle. The second part (Chapters 9-12) considers statistics on the spheres of arbitrary dimension. The third part (Chapters 13-14) treats extensions to general manifolds, shape analysis and complex projective spaces. Thoughout the book, the theory is illustrated by practical examples, charts and diagrams. Formulae for Bessel and Kummer functions, statistical tables and a list of notation are given in the appendices.

Contents:
1. Some general concepts
2. Avoidance of bias
3. Control of haphazard variation
4. Specialized blocking techniques
5. Factorial designs: Basic ideas
6. Factorial designs: Further topics
7. Optimal design
8. Some additional topics
APPENDIX A: Statistical Analysis
APPENDIX B: Some Algebra
APPENDIX C: Computational Issues

Readership: General audience concerned with statistics in experimental fields with some knowledge of and interest in theoretical issues

This long awaited book is in the spirit of the classic introductory text by D.R. Cox (Planning of Experiments, 1958, Wiley) in emphasizing design concepts, often approached through intuitive explanations, rather than mathematical detail. The result is a compact and insightful presentation of an unusually wide range of design areas important for industrial and agricultural experiments, and clinical trails. Topics include randomization and retrospective adjustment for bias, traditional block designs, cross-over designs, confounding and split-plot designs, Taguchi methods, non-linear design, space filling designs, and Bayesian and adaptive designs. Illustrations of how particular design concepts arise in practical situations are an especially useful feature; more detailed examples of real applications are also included. Bibliographic notes and references to recent books and some pertinent papers are given in every chapter together with exercises.
The book will be particularly useful for statisticians who want to learn about design theory linked to practical problems, and for advanced undergraduate and postgraduate students. Whilst much will be accessible to the intended audience, some of the more technical sections require considerable confidence and experience in mathematics and statistical theory for a full appreciation.
This book is usefull in its focus on design, rather than analysis, of experiments. Analyses are presented in the main text, when needed, assuming knowledge of linear models and analysis of variance. A review of these areas, and S-PLUS code for analyzing the examples, are reserved for an appendix. This approach enables a clear presentation of key ideas in the main areas of design, and gives an interesting and enjoyable read.

Contents
1. Basic principles and experiments with a single factor
2. Experiments with more than one factor
3. Full factorial experiments at two levels
4. Fractional factorial experiments at two levels
5. Full factorial and fractional factorial experiments at three levels
6. Other design and analysis techniques for experiments at more than two levels
7. Nonregular design: Construction and properties
8. Experiments with complex aliasing
9. Response surface methodology
10. Introduction to robust parameter design
11. Robust parameter design for signal-response systems
12. Experiments for improving reliability
13. Experiments with nonnormal data
Appendices: Statistical tables, including critical values for Lenth's method for analysis of unreplicated factorials

Readership: Experimenters in science and engineering, final-year undergraduate and master students in statistics, PhD students in statistics or any experimental science

It has taken a while, but Taguchi methods are now mainstream statistics. This book integrates a fairly standard statistical treatment of factorial experimentation with a clear presentation of the best ideas from Taguchi. It is a statistics text, not an experimenter's cookbook. The overall level is about right for a masters student in statistics, although with judicious selection of material it would be appropriate for courses and readers at other levels. Some background in statistics, preferably up to multiple regression and ANOVA, and at least some acquaintance with matrix algebra would seem to be desirable prerequisites. The authors have been very active in research in this area in recent years, and some of the other material, Chapter 8 for example, reflects this. A skim through selected parts of this book would make a good refresher course for anyone wishing to catch up on recent developments. It is an impressive volume that seems likely to become a standard text.

Contents:
1. Introduction
2. One-way classification
3. Two-way crossed classification without interaction
4. Two-way crossed classification with interaction
5. Three-way and higher-order crossed classifications
6. Two-way nested (hierarchical) classification
7. Three-way and higher-order nested classifications
8. Partially nested classifications
9. Finite population and other models
10. Some simple experimental designs
11. Analysis of variance using statistical computing packages

This text covers the analysis of variance for observations that can be described by normal theory models with fixed effect terms, random effects terms or a mixture of both fixed and random effects. The theory for these three model types is developed for increasingly complicated situations, chapter by chapter, from one-way classification through two-way classification, with and without interaction, to higher-order nested and partially nested classifications. The development is very detailed, and the first chapter after the short introduction on one-way classification models takes one hundred and twelve pages, covering point and interval estimation, multiple comparisons, verification of assumptions, computer applications, worked samples and a comprehensive set of exercises. This pattern is followed for the other situations up to a four-factor partially nested classification with the first three factors nested and the fourth factor crossed with the other three. All chapters have illustrative examples carried out using one or more of the statistical analysis packages, SAS, SPSS and BMDP. In addition, a chapter is included which describes in more detail the use of these systems to produce the analyses discussed. There is an extensive list of references, but perhaps the book's most useful features are the appendices that contain a wide range of distributional results and a wealth of tables and charts. These include the percentage points of standard distributions, tables and charts for powers of various tests, sample-size tables, critical values of various multiple comparison tests and tests for skewness and kurtosis, tables to test for normality, operating characteristic curves and charts for sample size determination for the one-way classification. The book could serve as a useful reference source for theoretical and practical examples.

Contents:
1. Introduction
2. Clarify the objective
3. Summarize beliefs and uncertainties
4. Decide on a strategy
5. Plan a single experiment
6. Design the experiment
7. Collect the data
8. Update beliefs and uncertainties
9. Revisit the objective

This is one of the most enjoyable books that I have read in a long while and is intended primarily for people who will conduct experiments. Written by a statistician who believes that the non-statistical aspects of planning and conducting experiments are more important than the formal design and analysis, the text concentrates on questions for which there are no uniquely correct answers. Topics are presented and discussed in the order in which they might be considered when planning and conducting a programme of experiments, rather than in order from mathematically simple to mathematically complex. The book is not intended as an introductory text but a glossary is provided to remind the reader of standard concepts and terms. A section on the use of spreadsheets for data recording, however, presents a number of time-saving hints and tips for those new to computer-based data-recording. The author does not discuss computer programs but does highlight some issues and problems that are associated with analyzing data. Finally, guidance is provided for the non-statistician on when to seek professional assistance with the analysis of a particular experiment.

Contents:
1. Biostatistics and biomedical science
2. Relative risk estimates and tests for two independent groups
3. Sample size, power and efficiency
4. Stratified-adjusted analysis for two independent groups
5. Case-control and matched studies
6. Applications of maximum likelihood and efficient scores
7. Logistic regression models
8. Analysis of count data
9. Analysis of event-time data
Appendix: Statistical Theory

This is an excellent textbook for an advanced course in biostatistics and also an indispensable reference for biostatisticians and epidemiologists. The focus is, as the title states, on how to estimate and to make inference on relative risk measures. Three are studied in detail: the risk ratio, the odds ratio and the rate ratio. As with most textbooks on the subject, these measures are discussed in the context of cross-sectional, prospective and retrospective sampling, where matching could also be a feature. However, what makes this textbook so valuable is that it covers the core methods first using classical statistical tools and then likelihood-based theories, highlighting the continuities. Another important feature is the care and balance with which it is drafted: the reasoning is always clear, the mathematical presentation detailed but to the point, the examples linked across different chapters. Further the data used in the examples are fully available via the web and occasionally SAS instructions and outputs are given and discussed. A chapter deserving special mention is "Sample size, power and efficiency" for its comprehensive and clear review of the principles inter-relating power and efficiency calculations. One minor criticism goes to the use of the term "relative risk" to indicate the whole class of measures of effect as well as more specifically the risk ratio.

Contents:
1. Introduction
Part I: Data Familiarisation and Presentation
2. Exploring, summarising and presenting data
3. Reliability, probability and confidence
4. Sampling
Part II: Questions of Comparison
5. Single sample comparison
6. Comparing two samples
7. Multiple comparison
Part III: Sequential Relationships
8. Non-causal and causal relationships
Part IV: Questions of Association and Agreement
9. Tabular relationships
Concluding remarks

Answers to scientific questions are often obtained through methodical, lengthy and exciting endeavour. Without well-defined aims, scientific investigation becomes pointless. This book takes the reader through the structured steps necessary for quantitative investigations. The text is suitable for those students with limited knowledge and ability with mathematics but who may, nonetheless, wish to use statistical techniques appropriately. The reference list is rather limited and dated which might deter the inquiring student from further study. The text covers the basic statistical concepts, methods and techniques without the need for lengthy mathematical derivations. Analyses are illustrated by full-worked examples and the author discusses the type of biological question to which each technique should be applied. The text will be a useful starting point for students of applied statistics who need to integrate their studies with Minitab. The end of each chapter provides a summary of the Minitab commands introduced and dialog boxes from Minitab are included in the text, as appropriate.

Contents:
1. An overview
2. Illustrative cases and data sets
3. Collection and preliminary analysis of failure data
4. Probability distributions for modeling time to failure
5. Basic statistical methods for data analysis
6. Modeling failures at the component level
7. Modeling and analysis of multicomponent systems
8. Advanced statistical methods for data analysis
9. Software reliability
10. Design of experiments and analysis of variance
11. Model selection and validation
12. Reliability management
13. Reliability engineering
14. Reliability prediction and assessment
15. Reliability improvement
16. Maintenance and unreliable systems
17. Warranties and service contracts
18. Reliability optimization
19. Case studies
20. Resources materials

This book provides a comprehensive overview of both qualitative and quantitative aspects of reliability. Mathematical and statistical concepts related to reliability modeling and analysis are presented along with important qualitative tools and managerial issues. There is an extensive bibliography and a listing of resources which includes journals, reliability standards, other publications, and data bases. The coverage of individual topics is not always deep, but this should be a valuable reference for any engineer or statistician working in reliability.

Contents
Part I: First Steps
1. Getting started
2. Descriptive statistics
3. Graphics
4. Regression methods
5. Teachware quantlets
Part II: Statistical Libraries
6. Smoothing methods
7. Generalized linear models
8. Neural networks
9. Time series
10. Kalman filtering
11. Finance
12. Microeconomics and panel data
13. Extreme value analysis
14. Wavelets
Part III: Programming
15. Reading and writing data
16. Matrix handling
17. Quantlets and quantlibs

Readership: Students, teachers and researchers interested in computer-aided statistical data analysis

This book is a guide for the use of the statistical package "XploRe". The statistical package "XploRe" requires the user to complete the special commands for the data procedures. Users, who are using other statistical packages with good spreadsheets and databases with an advanced menu system, will not be pleased with this. On the other hand, this package has some good features. It has a good library of statistical methods, for example, Kalman filtering, extreme value analysis and analysis of wavelets. The authors have included modules for finance analysis, micro-econometrics and panel data analysis that may be of interest to teachers and students in economics and business. The book is written in a good style and there is a bibliography for each chapter. The student version of the package is accompanied by a CD disk. I tested some of the modules of the package and found them to be good.

Contents:
1. Introducing matrices
2. Determinants
3. Inverse matrices
4. Linear dependence and rank
5. Simultaneous equations and generalized inverses
6. Linear spaces
7. Quadratic forms and eigensystems
8. Other topics
Appendix A: Matrix Calculations
Appendix B: Some Matrix Algoritms

Readership:Applied statisticians and other users of statistical methods, students of statistics

This book succeeds admirably in its aim of presenting 'those parts of matrix theory and their applications… useful to statisticians' in a way to meet the needs of non-specialist users of matrix methods. This 2nd edition has some 60% more pages than the first edition [1986, Short Book Reviews, Vol. 7, p. 25], partly due to an improved typeface and layout, but much more importantly to the thorough rewriting of the text in a reader-friendly, sometimes conversational, style, with ideas and arguments explained in a clear unhurried way. There is also some new material, mainly consisting of a new chapter 'Other topics' which include vectorizing, Jacobians, Hessians, Hermitian and unitary matrices, quadratic forms in normal variates and Cochran's theorem. There are useful examples after each chapter (mostly the same as in the first edition), with solutions in most cases. All in all this new edition is highly recommended.

Contents
1. Introduction
2. Probability and random variables
3. Fundamental procedures
4. Asymptotic expansions
5. Expansions of expectations, cumulants, and unbiased estimates
6. Expansions of distributions
7. Expansions for likelihood quantities
8. The analytic bootstrap
9. Sample surveys
10. Intersection matrices

Increase in computational power in recent decades have allowed the development of algebraic systems for doing mathematics by computer. This book concerns symbolic algorithms and their application in statistical inference. It considers the development of fundamental algorithms and their application to different areas of statistical methodology, including likelihood inference, the bootstrap, sample surveys, Edgeworth and saddlepoint calculations. The focus of the writing lies in discussion of the foundations of the methodology, in particular in the definition and structure of a series of core operators, which could be implemented in a number of systems. The interested reader will, however, be able to enjoy immediately the implementation and application of the algorithms, through a series of Mathematica notebooks available from the first author's website, as described in the book.

Contents:
Part 1: Theory
1. Preliminary considerations
2. State of the art review
3. Retrospective methods of statistical diagnosis for random sequences: Change-point problems
4. Retrospective methods of statistical diagnosis for random processes: Contamination problems
5. Sequential methods of statistical diagnosis
6. Statistical diagnosis problems for random fields
Part 2: Applications
7. Applications of the change-point analysis to investigations of the brain electrical activity
8. Methods of statistical diagnosis in economic and financial systems
Appendix: Algorithms of Statistical Diagnosis

Readership: Mathematical statisticians, applied statisticians in biomedical engineering and econometrics

It is the opinion of the authors that statistical diagnosis should be at the beginning of any statistical research. The purpose is to investigate whether the data are generated by one or by many probabilistic sources. It is only in the case of a unique probabilistic data generating mechanism that effective application of classical statistical inference is possible. In this book the authors consider methods for statistical analysis of complex situations with many (a priori unknown) data generating mechanisms. The present book can be seen as an updating of a previous one by the same author (Nonparametric Methods in Change-Point Problems, 1993). The monograph is divided in a theoretical part (Chapters 1 to 6) and an applied part (Chapter 7, 8 and the Appendix). In the theoretical part, the important models for statistical diagnosis considered here are the change-point models (i.e. abrupt or gradual changes of probabilistic characteristics of the observations in the sample). Both problems are considered for random functions and for random fields. The applied part of the book starts with a special chapter (written by A.Ya. Kaplan and S.L. Shishkin) on the nonparametric analysis of human electroencephalogram (EEG) signals. Another important application is in the context of financial and econometric modelling. In the Appendix, the authors describe their specially developed program package Verdia. There is an extensive bibliography of three hundred and forty-three items. All this makes the book a valuable up-to-date mathematical treatment of the subject.

Contents:
1. Introduction
2. Theory of nonparametic mixture models
3. Algorithms
4. Likelihood ratio test and number of components
5. C.A.MAN-application: Meta-analysis
6. Moment estimators of the variance of mixing distribution
7. C.A.MAN-application: Disease mapping
8. Various C.A.MAN-applications
Appendix: Working with C.A.MAN

This book presents a selection of theoretical and algorithmic tools for handling mixture models that are becoming increasingly important for the modelling of unobserved population heterogeneity. Diagnostic tests for extra-population heterogeneity are discussed, contrasted and a correction presented to a long-standing test statistic. The software package C.A.MAN (Computer-assisted analysis of mixtures), developed by the author and his co-workers, is introduced and its application discussed throughout the book. This software should permit the interested reader to carry out mixture analysis of their own data with little difficulty and facilitate a better appreciation of the methods presented. Currently, there are a number of other packages and routines available for computing mixture distribution estimates and a selection of these are briefly reviewed. With regard to C.A.MAN, the program is menu driven and is more robust with respect to initial values than other packages. The application of meta-analysis to the question of homogeneity (or heterogeneity) of study results is investigated. Disease mapping in 2-D space with an additional time component is illustrated. The text is well written and easy to read.

Contents:
1. Conditional specification: Concepts and theorems
2. Exact and near compatibility
3. Distributions with normal conditionals
4. Conditionals in exponential families
5. Other conditionally specified families
6. Improper and nonstandard models
7. Characterizations involving conditional moments
8. Multivariate extensions
9. Estimation in conditionally specified models
10. Marginal and conditional specification in general
11. Conditional survival models
12. Applications to modeling bivariate extremes
13. Bayesian analysis using conditionally specified models
14. Conditional versus simultaneous equation models
15. Paella
Appendix A: Simulation
Appendix B: Notation

It is well known that marginal distributions do not characterize joint distributions, but what can we say if conditional distributions are available? If conditional distributions are known, will there exist a corresponding joint distribution, and if so, will it be unique? Do there exist bivariate distributions with all the conditional densities normal, which are not bivariate normal? In the Bayesian context, if conditional distributions are elicited from experts, and it is found that they are not compatible with a joint distribution, then how might one obtain a joint distribution to best match the conditionals in some sense?
This fascinating book provides the answers to these and many related questions, in a wide range of areas. It is a substantially updated version of the authors' monograph entitled "Conditionally Specified Distributions", published by Springer-Verlag in 1992 and contains a wealth of new material by the authors and others. The book is well written, and presents clearly an important and developing subject.

Contents:
1. Introduction
2. Model and distribution terminology
3. Variability and related curve properties
4. Moments and curve uncertainty
5. Goodness of fit
6. Variates, variables and regression
7. Mixing parameters and data-generation models
8. The association parameter ñ
9. Regression and association parameters
10. Parameters, confounding and least squares
11. Nonparametric adjustment
12. Continuous variate adjustment
13. Procedural road maps
14. Model-based and generalized representation
15. Parameters, transformations and quantiles
16. Noncentrality parameters and degrees of freedom
17. Parameter-based estimation
18. Interference and composite variates
19. Parameters and test statistics
20. Curve truncation and the curve e(x)
APPENDIX I: Models and notation
APPENDIX II: Variate independence and curve identity
APPENDIX III: General statistical and mathematical notation

This book is aimed at providing an introductory guide to statistical methodology and its underlying concepts for users of statistical methods in research and development. The author's approach is based on a framework which focusses discussion on the ideas of curves and individual parameters. The book deserves to succeed in providing the reader with key insights into both data acquisition and statistical interpretation. The style is refreshing. This is no cookbook, but instead an eloquent essay, based on a series of interdisciplinary lectures, on the fundamentals of statistical practice. It is a book which both rewards the reader and demands close concentration.

Contents:
1. Introduction
Part I: Deterministic Models
2. Multi-stage decision problems
3. Networks
4. Further applications
5. Convexity
Part II: Stochastic Models
6. Markov systems
7. Optimal stopping
8. Special problems
Part III: Markov Decision Processes
9. General theory
10. Minimising average costs
11. Statistical decisions

Readership: Mathematics/statistics undergraduate and MSc students and those who teach them, those working in operational research

This textbook has evolved from courses on the subject given by the author to mathematics undergraduates. Thus, it draws on his many years of experience in teaching this topic as well as on his considerable professional expertise in the area. It is ideally suited to its stated purpose as a student text. The prerequisites are the calculus, real analysis and introductory probability that mathematics/
statistics students cover in their first or second years of study. The material is carefully structured and presented with clear motivations and explanations. There are many illustrative examples and exercises given at the end of each chapter. Notes on the exercises, with hints on their solutions and answers, are given at the end of the book. A brief historical introduction to the subject is given in the Introduction. As is appropriate at this level, the list of references is short and mostly limited to other, related, textbooks rather than research papers.

Contents:
1. Introduction
2. Notation and definitions
3. Uniform laws of large numbers
4. First applications: Consistency
5. Increments of empirical processes
6. Central limit theorems
7. Rates of convergence for maximum likelihood estimators
8. The non-i.i.d. case
9. Rates of convergence for least squares estimators
10. Penalties and sieves
11. Some applications to semiparametric models
12. M-estimators

This book, which grew out of a doctoral course given by the author in 1996, deals with the asymptotic theory of M-estimators. Special attention is given to the two most important examples, maximum likelihood estimators and least squares estimators, for which an extensive account is given of the rate of convergence problem. The essential tool in this unified treatment is empirical process theory and the necessary material is included in the book. Also penalty and sieve methods are considered. The book is well written and provides a modern contribution to a very important class of nonparametric estimators. It will be appreciated by researchers in statistics who want to know the state of the art in this field. Another plus of the book is that each chapter ends with interesting notes and some challenging problems.

Contents
1. Introduction
2. Markov chain Monte Carlo sampling
3. Basic Monte Carlo methods for estimating posterior quantities
4. Estimating marginal posterior densities
5. Estimating ratios of normalizing constants
6. Monte Carlo methods for constrained parameter problems
7. Computing Bayesian credible and HPD intervals
8. Bayesian approaches for comparing nonnested models
9. Bayesian variable selection
10. Other topics

This book focuses on Monte Carlo methods for the estimation of the posterior parameters of densities. The main basis for the theory is Markov chain Monte Carlo estimation is given. The authors have investigated different topics in simulation methods of Bayesian estimation and modelling; estimating posterior quantities, model comparison and selection, variable selection and other topics. This book combines the theory topics with good computer and application examples from the field of food science, agriculture, cancer and others. The volume will provide an excellent research resource for statisticians with an interest in computer intensive methods for modelling with different sorts of prior information. Although there are many exercises, this is not an introductory book to Monte Carlo methods in Bayesian modelling. The mathematical prerequisites are high; it is possible to recommend it to PhD students with an interest in solving complex problems within the Bayesian paradigm.

Contents:
1. Reversibility and identifiability
2. Minimum phase estimation
3. Homogeneous Gaussian random fields
4. Cumulants, mixing and estimation for Gaussian fields
5. Prediction for minimum and nonminimum phase models
6. The fluctuation of the quasi-Gaussian likelihood
7. Random fields
8. Estimation for possibly nonminimum phase schemes

Linear time series are often treated in a linear way, and this sometimes requires one to pretend that the model is Gaussian. This book compares what is possible when the model is Gaussian with what is possible when it is not by addressing the issues that are frequently left on the sidelines of standard time series texts: reversibility, identifiability, different Markov properties, regularity versus singularity and entropy. Non-linear techniques for estimation and prediction appear naturally. These and other topics will make this book useful as a reference source to the more theoretical among time series specialists.

Contents:
1. Introduction
2. Fitting sinusoids
3. The search for periodicity
4. Harmonic analysis
5. The fast Fourier transform
6. Examples of harmonic analysis
7. Complex demodulation
8. The spectrum
9. Some stationary time series theory
10. Analysis of multiple series
11. Further topics

Readership: Students (undergraduate or graduate) of statistics or allied fields taking a course on time series methods; workers in the many fields in which time series data arise

The first edition of 1976 stood out as a model of how the theory of time series might be taught with great precision and lucidity at an introductory level. This new edition holds up very successfully while incorporating a quarter century of change. The content has been expanded to include more on complex demodulation and harmonic analysis. An important step has been to adapt to modern statistical computing practice: Fortran is out, S-plus is in, the Fast Fourier Transform is given less emphasis. Each of the time series used as examples are readily obtainable through the internet.
A disappointment is that the author did not apply his pedagogic skill to include a much needed introduction to the current next big thing in spectral analysis wavelets.
What I cannot understand is why the publishers have made this excellent textbook too expensive for widespread adoption by college level courses.

Contents:
1. Probability review
2. Discrete-time Markov models
3. Recurrence and ergodicity
4. Long run behavior
5. Lyapunov functions and martingales
6. Eigenvalues and nonhomogeneous Markov chains
7. Gibbs fields and Monte Carlo simulation
8. Continuous-time Markov models
9. Poisson calculus and queues

Readership: Students and researchers in operations research, electrical engineering, physics and biology

It is not easy to find good textbooks aimed at a non-mathematical audience in which Markov chain theory (discrete and continuous time, discrete state space) is treated together with serious fields of applications. This book indeed gives the former; for the latter Gibbs sampling and queueing applications are included. I particularly liked Chapter 7 (60 pages) on Gibbs fields and Monte Carlo simulation where for instance such topics as image restoration, simulated annealing and MCMC are discussed. The author's style of writing is fairly relaxed. Numerous examples and exercises are given. The book is fully self-contained. It will not only appeal to the intended readership, but also more generally makes an excellent text on which to base a course on applied stochastic processes.

Contents:
Part I: Theory
1. Single-period option pricing
2. Brownian motion
3. Martingales
4. Stochastic integration
5. Girsanov and Martingale representations
6. Stochastic differential equations
7. Option pricing in continuous time
8. Dynamic term structure models
Part II: Practice
9. Modelling in practice
10. Basic instrument and terminology
11. Pricing standard market derivatives
12. Futures contracts
Part III: Orientation: Pricing exotic European derivatives
13. Terminal swap-rate models
14. Convexity corrections
15. Implied interest rate pricing models
16. Multi-currency terminal swap-rate models
Part IV: Orientation: Pricing exotic American and path-dependent derivatives
17. Short-rate models
18. Market models
19. Markov-functional models
Appendix 1: The Usual Conditions
Appendix 2: L2 Spaces
Appendix 3: Gaussian Calculations

Readership: Mathematical practitioners and academic mathematicians with an interest in real-world problems associated with financial derivatives

Many books on financial derivatives have appeared in recent years. This one adopts the mathematics text style of approach, with theorems and proofs. But, it is not a dry book. In particular, the authors adopt the strategy of outlining what they are going to do before getting down to the nitty gritty. This helps one keep one's sense of direction amongst the details. The book begins by pointing out that there are two reasons for the increase in interest in this area over the last thirty years: One is the need for organizations to control financial risk, and the other is the fact that the groundwork of the necessary mathematics had been laid in preceding decades. The book is divided into two parts, dealing respectively, with the theory of mathematical finance and the practical aspects. The book is deep and detailed, though the authors do take pains to point out the impossibility of being comprehensive.

Contents:
1. Nonequilibrium statistical mechanics
2. The Boltzmann equation
3. Liouville's equation
4. Boltzmann's ergodic hypothesis
5. Gibbs' picture: Mixing systems
6. The Green-Kubo formulae
7. The Baker's transformation
8. Lyapunov exponents, Baker's map and toral automorphisms
9. Kolmogorov-Sinai entropy
10. The Frobenius-Perron equation
11. Open systems and escape rates
12. Transport coefficients and chaos
13. Sinai-Ruelle-Bowen (SRB) and Gibbs measures
14. Fractal forms in Green-Kubo relations
15. Unstable periodic orbits
16. Lorentz lattice gases
17. Dynamical foundations of the Boltzmann equation
18. The Boltzmann equation returns
19. What's next?

Readership: Graduate students and researchers, with a background in statistical mechanics, working in condensed matter physics, nonlinear science, theoretical physics, mathematics and theoretical chemistry

This is Volume 14 in the Cambridge Lecture Notes in Physics. The book began its life as a set of lecture notes for a fourth year course at the Institute for Theoretical Physics at the University of Utrecht. The fundamental problem addressed is that of 'the reconciliation of the apparent irreversible behaviour of macroscopic systems with reversible, microscopic laws of mechanics which underlie this macroscopic behaviour'. This problem is classical in origin and the purpose of this book is to give understanding of this and of recent developments through dynamical chaos leading on to current research topics and a growing literature.

Contents:
1. Markov processes
2. Time reversal and duality
3. Non-relativistic quantum theory
4. Stationary Schrödinger processes
5. Construction of the Schrödinger processes
6. Markov processes with jumps
7. Relativistic quantum particles
8. Stochastic differential equations of pure-jumps
9. Variational principle for relativistic quantum particles
10. Time dependent subordination and Markov processes with jumps
11. Concave majorants of Lévy processes and the light cone
12. The locality in quantum physics
13. Micro statistical theory
14. Processes on open time intervals
15. Creation and killing of particles
16. The Itô Calculus

This book presents an account of the author's work aimed at establishing quantum physics on a basis of stochastic process theory. The author, who is a well-known specialist in stochastic analysis, takes his cue from a paper by Schrödinger (1931) on representation and reversibility of stochastic processes and develops ideas from that paper in the light of modern probability theory.
Does the author succeed in his ambitious aim?
I think not. In fact, the work appears to be carried out rather in isolation from present day thinking in quantum theory (most of the references to the physical literature are quite old), and this book as regards recent developments in the theory of quantum instruments and continuous in time nondemolition experiments, due to Kraus, Davis, Qzawa, Belavkin, Barchielli and Holevo (see, for instance, Barchielli and Holevo (1995); also Percival (1998)) and the questions of hidden variables and nonlocality. Today, most leading physicists regard the quest for hidden variables unnecessary and most likely futile, and they consider nonlocality as a well documented fact. Actually, the nonlocality aspect of the quantum world is presently being exploited in a variety of essential new experiments and techniques. By contrast, Nagasawa argues for hidden variables and against nonlocality.
As already indicated, the book is to a very large extent based on Nagasawa's own work. Correspondingly, the writing style is somewhat idiosyncratic, and the main thrust of the author's thinking is not easily discerned. Readers will likely find it useful to have the monograph by Aebi (1996) at hand when studying the book under review here. All in all this is a book of quite specialized interest.
Aebi, R. (1996): Schrödinger Diffusion Processes.
Basel: Birkhäuser.
Barchieli, A. and Holevo, A.S. (1995): Constructing quantum measurement processes via classical calculus.
Stoch. Proc. Appl. 58, 293-318.
Percival, I. (1998): Quantum State Diffusion.
Cambridge University Press.

Contents:
PART I : S4 Deployment Strategy Phase
1. Six sigma overview and implementation
2. Knowledge-centered activity (KCA) focus and process improvement
PART II : S4 Measurement Phase
3. Overview of descriptive statistics and experimentation traps
4. Process flowcharting/process mapping
5. Basic tools
6. Probability
7. Overview of distributions and statistical processes
8. Probability and hazard plotting
9. Six sigma measurements
10. Basic control charts
11. Process capability and process performance
12. Measurement systems analysis (Gauge repeatability and reproducibility—gauge R&R)
13. Cause-and-effect matrix and quality function deployment
14. Failure mode and effects analysis (FMEA)
PART III : S4 Analysis Phase
15. Visualization of data
16. Confidence intervals and hypothesis tests
17. Inferences: Continuous response
18. Inferences: Attribute (pass/fail) response
19. Comparison tests: Continuous response
20. Comparison tests: Attribute (pass/fail) response
21. Bootstrapping
22. Variance components
23. Correlation and simple linear regression
24. Single-factor (one-way) analysis of variance
25. Two-factor (two-way) analysis of variance
26. Multiple regression
PART IV : S4 Improvement Phase
27. Benefiting from design of experiments (DOE)
28. Understanding the creation of full and fractional factorial 2k DOEs
29. Planning 2k DOEs
30. Design and analysis of 2k DOEs
31. Other DOE considerations
32. Variability reduction through DOE and Taguchi considerations
33. Response surface methodology
PART V: S4 Control Phase
34. Short-run and target control charts
35. Other control charting alternatives
36. Exponentially weighted moving average (EWMA) and engineering process control (EPC)
37. Pre-control charts
38. Control plan and other strategies
39. Reliability testing/assessment: Overview
40. Reliability testing/assessment: Repairable system
41. Reliability testing/assessment: Nonrepairable devices
42. Pass/fail functional testing
43. Application examples
APPENDIX A: Equations for the Distributions
APPENDIX B: Descriptive Information
APPENDIX C: DOE Supplement
APPENDIX D: Reference Tables

Readership: Practitioners who seek a reference for the entire field in a single volume, and students of applied statistics desiring a preview of current statistical practice in some industries

The phrase "Six Sigma" is a banner currently in vogue that denotes a knowledge-based strategy for quality improvement in industry, stressing waste reduction to return financial benefits to the company. Most of the methodologies subsumed by Six Sigma are well-established and had already found currency either in their own right as statistical methods or under the banners of earlier quality efforts such as TQM. However, the fundamentally "new" element of Six Sigma is the requirement that all quality measurements be expressed in terms of net financial benefit to the company so that the value of quality improvements can be tracked.
The origin of the phrase as an indicator of good quality has its roots in the normal distribution—for example, if the distance from the mean (of the population of individual product items) to the nearest specification limit for the product is six standard deviations, then the probability of an individual failure relative to those specifications is very low. In this case the product is said to have a "sigma quality level" of six. (Current convention allows a 1.5 standard deviation shift of the mean from the center of the specification range for determining sigma quality levels.) The concept of the sigma quality level as an index to compare processes is sometimes extended to non-normal populations by matching defect rates of the non-normal population to tail areas of a standard normal, and determining the implied number of (normal) standard deviations from the mean to that tail. However breathtaking this may be to statisticians, this approach to developing a common index to compare processes has won believers in management.
The author of the present book is an independent consultant, and the presentation is his systematization of the many statistical methods that can be useful. The notation S4 is his trade phrase ("Smarter Six Sigma Solutions"). The book is certainly a useful reference to dip into as needed, but would be daunting for non-statisticians to read from start to finish.
In the end, quality improvement is as much non-statistical as statistical. This book will give the practitioner a solid footing in the data-based aspects of the business.

Contents:
1. The learning methodology
2. Linear learning machines
3. Kernel-induced feature spaces
4. Generalisation theory
5. Optimalisation theory
6. Support vector machines
7. Implementation techniques
8. Applications of support vector machines
Appendix A: Pseudocode for the SMO algorithm
Appendix B: Background Mathematics

Readership: Machine learning students and practitioners who want a gentle but rigorous introduction to this class of learning systems

In the 1960s a new class of algorithms (that is, one which was different from the linear discriminant method developed earlier in the 1930s by Fisher) was developed for fitting linear decision surfaces in supervised classification problems. This method was based on sequentially updating the parameter estimates as new data points were presented: it was a 'learning' algorithm. Models based on this approach, though having the same linear form as those based on Fisher's method were known as perceptrons. Gradually, over time, research in this area began to develop in two, quite distinct, directions. One led to the development of feedforward neural networks, and the other led to the development of support vector machines. Neural networks overcome the limitations of the simple linear decision surface of the perceptron by introducing nonlinear transformations into the process, yielding nested series of linear combinations of nonlinear transformations of linear combinations of the raw variables. In contrast, support vector machines transform the raw variables into a high-dimensional space of derived variables, and then fit a linear decision surface in this space. The choice of decision surface is based on finding that separating surface which is maximally distant from the nearest points in each class (the 'support vectors') in this high-dimensional space.
In itself this is all very interesting, but the power and particular interest of support vector machines arises because a mathematical trick means that it is possible to sidestep the explicit transformation into the high-dimensional space: in fact, the key aspects of the classification decisions can be represented in terms of a kernel function based on inner products of the transformed representations of the data points. This book describes this approach. It is the most accessible introduction to the area I have yet seen. It includes exercises, and also pointers to website software sources – an essential for a book dealing with material at the cutting edge of statistics, computing and machine learning. Applications of the methods have been made in a number of areas and the accumulating evidence is that such methods can be highly effective. Moreover, the work in this area, like that in neutral networks some years before, has yielded deep insights into problems of generalization.

Contents:
1. Introduction
2. Some basic concepts
3. Algorithms for sampling
4. Asymptotic approximations
5. Multiple quadrature
6. Independent importance sampling
7. Markov chain methods

Readership:Statisticians, numerical analysts, mathematicians and scientists who need to evaluate integrals

This volume is both a good textbook and a useful reference. It surveys a wide variety of different ways of numerically evaluating integrals. The authors believe that "all of the methods that (they) discuss should be part of the practitioner's toolkit". An underlying theme is that integrating methods are often complementary rather than competing. The main emphasis is on higher-dimensional integrals, though the lower-dimensional case is well covered. Approximately half the book is devoted to Monte Carlo methods. The multivariate normal distribution plays an important role in this book, as does Bayesian statistics. For each method considered, the basic theory is given and discussed (usually at some length) as well as the practical issues (including error analysis). There is a set of exercises at the end of each chapter; these are largely concerned with verifying points of the theory mentioned in the text. The authors' aim was to make their exposition sufficiently complete to ensure that the reader will only rarely need to consult other references in order to understand a method. Their target audience is "physical and mathematical scientists who face challenging integration problems"; hence a good, broad mathematical background (including probability and statistics) is assumed. The bibliography is quite extensive (300 or so items) and really up-to-date.

Contents:
1. Concepts of spatial pattern
2. Sampling
3. Basic methods for one dimension and one species
4. Spatial pattern of two species
5. Multispecies pattern
6. Two-dimensional analysis of spatial pattern
7. Point pattern
8. Pattern on an environmental gradient
9. Conclusions and future directions

Readership: Graduate students, teachers and researchers in the fields of vegetation science, conservation biology and applied ecology; statisticians interested in developing methodology to be used for applied spatial pattern analysis

This book describes and evaluates some stochastic techniques for detecting and quantifying a variety of characteristics of spatial pattern in plant ecology. It also discusses the concepts on which these techniques are based. Blocked quadrat variance and its extensions, multiscale ordination, correspondence analysis, variograms, semivariogram and fractal dimension, two-dimensional spectral analysis, bivariate Markov and point processes are some of the techniques used.
Many illustrative examples from real field studies and worked examples together with various figures help guide the reader through the text. Mathematical details have been left out. But at each chapter most of the major aspects of the methods presented including their usefulness and limitations are clearly presented and critically discussed in the context of their applications in the field of plant ecology.
The author briefly refers to the importance of "LANDSAT" and of "Geographic Information System" in future developments of the spatial pattern analysis in plant ecology. Wavelet analysis is also a promising tool that has been only briefly mentioned in the book. Bayesian methods have not been clearly mentioned at all.
In conclusion, the book reveals in detail how stochastic methods can be used to solve relevant spatial pattern problems in plant ecology, stresses the need for new techniques to be developed and points out some promising research directions. Overall the author has achieved his goal. I also think the book can provide the statistician with a considerable challenge.

Contents:
1. Preliminaries
2. Structural analysis
3. Kriging
4. Intrinsic model of order k
5. Multivariate methods
6. Nonlinear methods
' 7. Conditional simulations
8. Scale effects and inverse problems

Readership: Professional geostatisticians, statisticians working in the earth sciences, students of spatial statistics

This is a comprehensive account of the geostatistical techniques developed by the Fontainebleau school, of which the authors have been prominent members. Although this is a book in the Wiley Probability and Statistics series, it is entirely grounded in the geostatistics literature. Its topic is spatial interpolation and smoothing using spatial stochastic process models. The material of the first six chapters is covered in a number of other geostatistics books, but I found this one substantially less doctrinaire and so expect it to be more accessible to statisticians. It does include parts of case studies, although I would have appreciated more and I found the very dense contour maps hard to visualize. I really appreciated Chapter 7, which provides a very well-balanced view of the simulation of spatial processes with lots of instructive simulated images.
It seems that the writing of this book has taken many years, and the references from the last five chapters are scarce. That seems no great drawback, but it would have been nice to have included some of the case studies done with modern visualization techniques, for example of oil reserves.

Contents:
1. Discrete time Markov chains
2. Stationary distributions of a Markov chain
3. Continuous time birth and death Markov chains
4. Percolation
5. A cellular automation
6. Continuous time branching random walk
7. The contact process on a homogeneous tree
APPENDIX: Some Facts about Probabilities on Countable Spaces

This book takes an interesting modern approach to the classical results on Markov processes, using coupling arguments for example. It aims to be accessible to those with only a calculus education, although I think such readers would find it hard work. The 'spatial' in the title is perhaps something of an exaggeration as the processes discussed in the last four chapters are on graphs rather than in space, and are some of the simpler examples studied in rigorous statistical physics.
Given its modest requirements, this is not a reference work but a well-motivated introduction to both classical and recent work.

Contents:
1. The tools of statistical inference
2. Distribution theory for count data
3. Binary contingency tables
4. Binomial regression models
5. Smoothing binomial data
6. Poisson regression models
7. Conditional inference

This book started life as a lecture course at La Trobe University, and it is designed for MSc-level students. There are many varied and interesting exercises for each chapter except the last. The book is extended by a world-wide website, containing solutions to exercises, short manuals for computer packages, etc. Some of the exercises reference data and computer programs from the website. Throughout, the work is illustrated by output from computer packages. GLIM, MINITAB, S-PLUS, StatXacT and LogXact are used. By comparison, Agresti (1996), for example, uses SAS and SSPS. The style of writing is attractive, and makes the subject matter accessible. In addition to the classical material, there is detailed coverage of such modern and important areas as smoothing binomial data, ordinal data, quasi-independence and conditional inference. Each chapter concludes with interesting critical sections on Further Reading, in a similar style to Agresti (1990)'s Chapter Notes, for example.
This book will be very useful as an informed and thought-provoking source of reference, as well as a text for a lecture course.
Agresti, A. (1990). Categorical Data Analysis. New York: Wiley. [Short Book Reviews, Vol. 10, pp. 46].
Agresti, A. (1996). An Introduction to Categorical Data Analysis. New York: Wiley. [Short Book Reviews, Vol. 16, pp. 44].

Contents:
1. Modelling the error for directly measured observations
2. Estimation of parameters of probability distributions
3. Comparison of means
4. Uncertainty in the final result
5. Calculation and use of calibration curves

Readership: Scientists, engineers and managers concerned with producing accurate measurements in toxicology, earth sciences, chemistry, physics, environmental sciences, nuclear science, biology and other areas

This book is a joint work by the Commission for the establishment of methods of analysis of the Commissariat à l'Energie Atomique. Scientific progress involves a leapfrogging act between theoretical development and practical experimentation. The history of science shows that a key role in practical experimentation is played by enhanced accuracy of measurement. This book aims to teach readers how to use basic statistical methods to assess (and hence improve) the accuracy of measurements.
In content, it is essentially a basic statistics book, but with an orientation towards measurement accuracy. As such, it covers statistical staples as parameter estimation, analysis of variance, experimental design, regression, and so on.
Although it could be used as a text, it is dense, and would probably be more effective as a reference book (though it does contain plenty of examples).
The style and content struck me as rather old-fashioned. In particular, no acknowledgement seems to be made of the computational revolution in statistical data analysis which has occurred over the last two decades. This is doubtless a consequence of the desire to present all calculations "so that they can be carried out with limited resources (for example, any presentation involving matrices has been avoided)", but it means that, to take just an example, the dramatic developments in nonparametric regression and calibration curves of recent years are not described.

Contents:
PART I : Introduction
1. Basic concepts
2. Fundamentals of modelling
3. Multivariate models
PART II : Continuous Measurements
4. Heterogeneous populations
5. Longitudinal studies
6. Non-normal responses
PART III: Categorical and Count Data
7. Overdispersion
8. Longitudinal discrete data
PART IV: Duration Data
9. Frailty
10. Event histories
PART V: Planning a Study
11. Design issues
12. Modelling missing data and dropouts
APPENDIX A : Data Tables for the Examples
APPENDIX B : Data Tables for the Exercises

Readership: Research statisticians in agriculture, medicine, economics and psychology, and consulting statisticians who need an up-to-date account of the topic

The first edition of this book appeared only six years ago [Short Book Reviews, Vol. 14, pp. 25]. Since then, the area of repeated measures analysis has been the focus of a huge amount of research. This is reflected in the twenty-five per cent increase in the length of the book—and this despite a reduction of the number of references from 1,382 to 297 in recognition of the impossibility of providing a complete bibliography.
The book has been widely revised throughout, but this is particularly apparent in the categorical and duration data sections. The growth in computing power over the years since the first edition means that models which were fitted by approximate methods in the first edition, can now be fitted exactly. Nonlinear models are used more widely. The section on generalized estimating equations has been removed ("although such methods are still widely used, they have not stood the test of time. Better exact models are available"), and chapters on models for continuous non-normal data, on design issues specific to repeated measures, and on missing data and dropouts have been added. Changes such as these make this a valuable, practical book. Yet another change is that all likelihoods include the normalizing constants, so that some of the conclusions about model choice based on AIC (Akaike information criterion) differ from those of the previous edition. Exercises have been added.
In summary, this is probably the most comprehensive book on repeated measures currently on the market. It is one of those books from which most of us could learn much about statistical modelling in general, as well as about the specific topic of repeated measureS.
Some remarks Lindsey makes in his Preface to the second edition are of sufficient general importance to the statistical community that they bear repeating here. He says: "As with several of my books, much of the most interesting new material comes from articles rejected by well-known statistical journals. As a group, statistical referees tend to be very conservative: a minor modification to some obscure score test is revolutionary whereas a new family of models must either already be widely known or be wrong." In view of the innovations and developments in statistical ideas being made by researchers in other disciplines, these are points of which it would do us well to take note.

Contents:
1. Introduction
2. Univariate linear stochastic models: Basic concepts
3. Univariate linear stochastic models: Further topics
4. Univariate non-linear stochastic models
5. Modelling return distributions
6. Regression techniques for non-integrated financial time series
7. Regression techniques for integrated financial time series
8. Further topics in the analysis of integrated financial time series

There has been a great deal of empirical work on financial time series in recent years, which has utilized an enormous variety of statistical models. This book provides a coherent introduction to many of these models, some of which are of quite recent origin. The book will certainly be of value to practitioners as well as to students, in part because the list of references is extensive and up-to-date. Many of the techniques are illustrated by empirical applications, often to data from the United Kingdom. Numerous figures make many of the empirical results more accessible. Because the data are available from the author's web site, students can replicate the empirical work and try out alternative models.

Contents:
1. An introduction to empirical modeling
2. Probability theory: A modeling framework
3. The notion of a probability model
4. The notion of a random sample
5. Probabilistic concepts and real data
6. The notion of a non-random sample
7. Regression and related notions
8. Stochastic processes
9. Limit theorems
10. From probability to statistical inference
11. An introduction to statistical inference
12. Estimation I: Properties of estimators
13. Estimation II: Methods of estimation
14. Hypothesis testing
15. Misspecification testing

Readership: Students at second year undergraduate level and above studying econometrics and economics, students in other disciplines which make extensive use of observational data

This book is an attempt to give a framework for the modeling of observational data as opposed to experimental data. The author has reworked a course, enthusiastically received by students with no more than a basic familiarity with descriptive statistics, which embraces sigma-fields, stochastic conditioning, functional limit theorems, etc. How does he do it?
Is it the informality in the writing? ("A random variable is as 'big' as its standard deviation." [p. 108] ). ("The taking out what is known property." [p. 364] ).
Is it the relaxed way with definitions? ("The term standard error is often used in place of standard deviation." [p. 109] ). The probability mass function is everywhere called "the density function."
Is it the use of examples that are too easy? (The need to integrate out from a joint distribution to obtain the marginals is illustrated by integrating out from the joint distribution of two independent (yes, independent) exponentials. [p. 156] ). The derivation of the marginals of a bivariate normal is "rather involved (and thus omitted)." [p. 156] ).
Is it the finesse in handling mathematics? (A hash is made of finding the moments of an exponential random variable. [p. 110] ... and the cdf of the sum of two independent exponentials. [p. 590] ).
Is it because nearly all the exercises test only recall, with no manipulation of formulae or data? ("Explain the notion of an ordered sample." [p. 185] is typical).
Many of the pages are disfigured by displayed formulae having wrong font sizes, wrong subscripts and wrong limits. I say "Cauchy-Swartz" (sic, p. 423) to such sloppy publishing.

Contents:
1. Introduction
2. Elements of inference
3. Prior distribution
4. Estimation
5. Approximate and computationally intensive methods
6. Hypothesis testing
7. Prediction
8. Introduction to linear models

The subtitle of this book refers to the fact that it covers both the frequentist and Bayesian viewpoints on statistical inference. The classical topics of statistical inference (estimation, hypothesis, testing, prediction, linear models) are discussed under both main paradigms. The intermediate Chapter 5 makes the book particularly interesting. It discusses optimization algorithms (like Newton Raphson and EM) but also asymptotics and some simulation methods (like bootstrap and MCMC). The book is very adequate for use in a statistical inference class especially because of the appropriate level and the interesting and rich choice of exercises at the end of each chapter. The bibliography is relatively short and mainly consists of reference books rather than research papers.

Contents:
1. Semimartingales
2. Exponential families of stochastic processes
3. Asymptotic likelihood theory
4. Asymptotic likelihood theory for diffusion processes
5. Quasi likelihood and semimartingales
6. Local asymptotic behavior of semimartingale experiments
7. Likelihood and asymptotic efficiency
8. Inference for counting processes
9. Inference for semimartingale regression models
10. Applications to stochastic modeling
APPENDIX A : Dolean Measures for Semimartingales and Burkholder's Inequality for Martingales
APPENDIX B : Interchanging Stochastic Integration and Ordinary Differentiation and Fubini-Type Theorem for Stochastic Integrals
APPENDIX C : The Fundamental Identity of Sequential Analysis
APPENDIX D : Stieltjes-Lebesque Calculus
APPENDIX E : A Useful Lemma
APPENDIX F : Contiguity
APPENDIX G : Notes

This book focuses principally on continuous time models and is mostly concerned with establishing consistency and asymptotic normality (or variants such as mixed normality) of estimators, together with any associated optimality results. The treatment is rather austere, with little motivation and explanation, and arguments are often sketched or replaced by a reference. Specific applications are mostly mentioned briefly and rather incidentally. There is a huge amount of useful material in the book, including likelihood and quasi-likelihood based results and the treatment of parametric, semiparametric and nonparametric models, summarizing the state of the subject.

Contents:
Introductory Notes
1. Diffusion type processes
2. Parametric inference for diffusion type processes from continuous paths
3. Parametric inference for diffusion type processes from sampled data
4. Non-parametric inference for diffusion type processes from continuous sample paths
5. Non-parametric inference for diffusion type processes from sampled data
6. Applications to stochastic modeling
7. Numerical approximation methods for stochastic differential equations
APPENDIX A : Uniform Ergodic Theorem
APPENDIX B : Stochastic Integration and Limit Theorems for Stochastic Integrals
APPENDIX C : Wavelets
APPENDIX D : Gronwall-Bellman Type Lemmas

This book is closely related to the volume Semimartingales and their Statistical Inference [Short Book Reviews, Vol. 20, pp. 8] by the same author, diffusion processes being one of the significant subclasses for which the semimartingale formulation is useful. It is principally concerned with comprehensively cataloguing the diverse methods that are available for estimating parameters, in the parametric case, or the drift and diffusion in the nonparametric case, in diffusion type models.
Associated consistency and asymptotic normality results are provided whenever practicable. The treatment is rather austere, with little motivation and explanation, and arguments are often sketched or replaced by a reference. Specific applications are mostly mentioned briefly and rather incidentally. However, there is a substantial amount of useful material in the book for those concerned with statistical questions related to diffusion models.

Contents:
1. What is bootstrapping?
2. Estimation
3. Confidence sets and hypothesis testing
4. Regression analysis
5. Forecasting and time series analysis
6. Which resampling method should you use?
7. Efficient and effective simulation
8. Special topics
9. When does bootstrapping fail?

Readership: Professionals in engineering, the sciences, clinical medicine and applied statistics

This book is intended to provide an accessible introduction to application of bootstrap methods for readers who lack the mathematical background required by other texts on the subject. I imagine that it will be found pretty successful and useful. Some of the treatment is rather bald and derivative, and the material is discussed in a very matter of fact way. While it offers no new perspective on the applicability of bootstrap methods, the book is nevertheless enlivened by a series of interesting practical examples. A striking feature is the very extensive bibliography, which constitutes about a third of the bulk of the book. Though, naturally, this will rapidly become out of date, it is currently a most useful resource. The book provides a good coverage of topics. The anecdotal writing style will serve either to engage or irritate the reader, according to taste.

Contents:
Review of probability
1. Markov chains
2. Martingales
3. Poisson processes
4. Continuous-time Markov chains
5. Renewal theory
6. Brownian motion

Readership: Undergraduates or masters students who have had a course in probability theory, but not in measure theory

This is a first course on stochastic processes for students described under "Readership". The style is relaxed, rather stressing main ideas and intuition instead of fine mathematical detail; for most of the results, proofs are given. Numerous examples are given, together with more than three hundred and twenty-five exercises.
The topics treated are fairly standard for a course on applied stochastic processes. All in all, this is an accessible text which invites self-study.

Contents:
1. Introduction
2. Rao's inequalities and improvements
3. Orthogonal arrays and Galois fields
4. Orthogonal arrays and error-correcting codes
5. Construction of orthogonal arrays from codes
6. Orthogonal arrays and difference schemes
7. Orthogonal arrays and Hadamard matrices
8. Orthogonal arrays and Latin squares
9. Mixed orthogonal arrays
10. Further constructions and related structures
11. Statistical application of orthogonal arrays
12. Tables of orthogonal arrays
There is also a helpful appendix on Galois fields.

Readership: The authors say, Anyone who is running experiments...Anyone interested in one of the most fascinating areas of discrete mathematics...

I agree with the second statement under Readership, but I have doubts about the first. It would be good if every experimenter knew a lot about orthogonal arrays, but the mathematical demands of this book put it far out of reach of the average practitioner. Furthermore, the applications to design of experiments do not come until chapter eleven, by which time most of the non-mathematical readers will probably have given up.
With that reservation, it is a fascinating book for mathematicians. There is a feast of information and detail. For example, in the chapter on Hadamard matrices we are shown how to construct matrices of orders up to two hundred using the two methods of Paley and the method of Williamson. We are actually given in their entirety the five non-isomorphic matrices of order sixteen. Most experimenters have only heard of the version that is based on the factorial for four factors at two levels each. Again, the title of the following chapter promises to tell us only about Latin squares; but there is more than just an exhaustive discussion of sets of mutually orthogonal squares. We are told about F-squares (of which Latin squares are an interesting special case in which each symbol appears only once in each row and column).
It is a good book for mathematicians to read for their own edification. We are guided on our way with plenty of exercises at the ends of the chapters and by numerous examples. Every now and then, in the text, the authors pose research problems — questions on which work remains to be done.
Most experimenters come across little about orthogonal arrays except for two or three levels and strength one or two, and a few Graeco-Latin squares, taken from the Fisher and Yates tables. They have little or no realization of the applications to error-correcting codes. This book will bring them up to the frontier of a challenging field of applied algebra. I do not see it being used for a course, but it is good book for the mathematically inclined statistician, who is interested in experimental design, to have on the bookshelf.

Title	STATISTICAL EXPERIMENTAL DESIGN AND INTERPRETATION. An Introduction with Agricultural Examples.
Author	C.A. Collins and F.M. Seeney.
Publisher	Chichester, U.K.: Wiley, 1999, pp. vi + 280, £65.00.

Reviewer:
Institute	CEFAS Lowestoft Laboratory
Place	Lowestoft, U.K.
Name	C.M. O'Brien

Title	CLASSIFICATION, 2nd edition.
Author	A.D. Gordon.
Publisher	New York: Chapman and Hall/CRC, 1999, pp. x + 256, £49.00. [Original 1981, Short Book Reviews, Vol. 2, p. 3].

Reviewer:
Institute	University of Georgia
Place	Athens, Georgia, U.S.A.
Name	L. Billard

Title	A COURSE IN CATEGORICAL DATA ANALYSIS.
Author	T. Leonard with contributions by O. Papasouliotis.
Publisher	Boca Raton, Florida: Chapman and Hall/CRC, 2000, pp. viii + 183.

Reviewer:
Institute	University of Cape Town
Place	Rondebosch, South Africa
Name	J.M. Juritz

Reviewer:
Institute	University of Wisconsin
Place	Madison, U.S.A.
Name	N.R. Draper

Reviewer:
Institute	Imperial College of Science, Technology and Medicine
Place	London, U.K.
Name	E. McCoy

Reviewer:
Institute	University of Aberdeen
Place	Aberdeen, U.K.
Name	A. Lawson

Reviewer:
Institute	RIKEN Brain Science
Place	Wak-shi, Japan
Name	S. Amari

Reviewer:
Institute	University of Newcastle
Place	Newcastle, Australia
Name	G.C. Goodwin

Reviewer:
Institute	Statistics Canada
Place	Ottawa, Canada
Name	D.A. Binder

Reviewer:
Institute	University of Oxford
Place	Oxford, U.K.
Name	D. Coleman

Reviewer:
Institute	University of Reading
Place	Reading, U.K.
Name	R.N. Curnow

Reviewer:
Institute	SmithKline Beecham
Place	Collegeville, U.S.A.
Name	V.V. Fedorov

Reviewer:
Institute	Limburgs Universitair Centrum
Place	Diepenbeek, Belgium
Name	N.D.C. Veraverbeke

Reviewer:
Institute	Imperial College, Technology and Medicine
Place	London, U.K.
Name	D.J. Hand

Reviewer:
Institute	University of St. Andrews
Place	St. Andrews, U.K.
Name	A.W. Kemp

Reviewer:
Institute	University of Washington
Place	Seattle, U.S.A.
Name	R. Pyke

Reviewer:
Institute	Dartmouth Medical School
Place	Hanover, U.S.A.
Name	T.A. Stukel

Reviewer:
Institute	University College
Place	London, U.K.
Name	V.T. Farewell

Reviewer:
Institute	University of British Columbia
Place	Vancouver, Canada
Name	J.V. Zidek

Reviewer:
Institute	University of Southampton
Place	Southampton, U.K.
Name	P. Prescott

Reviewer:
Institute	niversity of Colorado
Place	Denver, U.S.A.
Name	R. Shanmugam

Reviewer:
Institute	SmithKline Beecham Pharmaceuticals
Place	Collegeville, U.S.A.
Name	S. Leonov

Reviewer:
Institute	University of Exeter
Place	Exeter, U.K.
Name	W.J. Krzanowski

Reviewer:
Institute	Katholieke Universiteit Leuven
Place	Heverlee, Belgium
Name	R. Boel

Reviewer:
Institute	Helsinki University, Central Hospital
Place	Helsinki, Finland
Name	H.M. Oksanen

Reviewer:
Institute	Stanford University
Place	Stanford, U.S.A.
Name	D. Siegmund

Reviewer:
Institute	University College London
Place	London, U.K.
Name	V.S. Isham

Reviewer:
Institute	ETH–Zürich
Place	Zürich, Switzerland
Name	P.A.L. Embrechts

Reviewer:
Institute	London School of Economics
Place	London, U.K.
Name	S. Powell

Reviewer:
Institute	South Bank University
Place	London, U.K.
Name	S. Starkings

Reviewer:
Institute	Queen's University
Place	Kingston, Canada
Name	J.T. Smith

Reviewer:
Institute	University of Essex
Place	Colchester, U.K.
Name	G.A. Barnard

Reviewer:
Institute	University of St Andrews
Place	St Andrews, U.K.
Name	C.D. Kemp