Short Book Reviews On-Line 2001

OPTIMIZATION: FOUNDATIONS AND APPLICATIONS.	R.E. Miller.
PUBLIC POLICY AND STATISTICS: CASE STUDIES FROM RAND.	S.C. Morton and J.E. Rolph (Eds.).
THE PURSUIT OF PERFECT PACKING.	T. Aste and D. Weaire.
Rutherford. Scientist Supreme.	J. Campbell, Foreword by M. Oliphant.
An Introduction To Cryptography.	R.A. Mollin.
Statistics for Environmental Science and Management.	B.F.J. Manly.
Applied Nonparametric Statistical Methods, 3rd edition.	P. Sprent and N.C. Smeeton.
Fundamentals of Modern Statistical Methods.	R.R. Wilcox.
Probability Essentials.	J. Jacod and P. Protter.
Combinatorial Methods in Density Estimation.	L. Devroye and G. Lugosi.
AN INVARIANT APPROACH TO STATISTICAL ANALYSIS OF SHAPES.	R.S. Lele and J.T. Richtsmeier.
Fitting Statistical Distributions.	Z.A. Karian and E.J. Dudewicz.
Probability and Statistical Inference.	N. Mukhopadhyay.
Practical Time series.	G. Janacek.
A Course in Time Series Analysis.	D. Peńa, G.C. Tiao and R.S. Tsay (Eds.).
Practical Statistics and Experimental Design for Plant and Crop Science.	A.G. Clewer and D.H. Scarisbrick.
Generalized, Linear, and Mixed Models.	C.E. McCulloch and S.R. Searle.
Introducing Anova and Ancova – A GLM Approach.	A. Rutherford.
Applying Regression and Correlation: A Guide for Students and Researchers.	J. Miles and M. Shevlin.
Applied Logistic Regression, 2nd edition.	D.W. Hosmer and S. Lemeshow.
Multidimensional Scaling, 2nd edition.	T.F. Cox and M.A.A. Cox.
Statistical Decision Theory.	S. French and D. Rios Insua. .
Structural Equation Modeling: Foundations and Extensions.	C. Kaplan.
Algebraic Statistics: Computational Commutative Algebra in Statistics.	G. Pistone, E. Riccomagno and H. Wynn.
Wavelet methods for time series analysis.	D.B. Percival and A.T. Walden.
Probability and Statistical Models with Applications.	C.A. Charalambides, M.V. Koutras and N. Balakrishnan (Eds.).
PROBABILITY VIA EXPECTATION, 4th edition.	P. Whittle.
PROBABILITY FOR STATISTICIANS.	G.R. Shorack.
STATISTICAL METHODS FOR QUALITY IMPROVEMENT, 2nd edition.	T.P. Ryan.
Optimal Reliability Design.	W. Kuo, V.R. Prasad, F.A. Tillman and C.-L. Hwang.
Statistical Methods for the Reliability of Repairable Systems.	S.E. Rigdon and A.P. Basu.
Statistical Analysis of Microstructures in Material Science.	J. Ohser and F. Mücklich.
Non-linear and Nonstationary Signal Processing.	W.J. Fitzgerald, R.L Smith, A.T. Walden and P.C. Young (Eds.).
Difference Equations with applications to Queues.	D.L. Jagerman.
Complex Stochastic Systems.	O.E. Barndorff-Nielsen, D.R. Cox and C. Klüppelberg (Eds.).
Weakly Dependent Stochastic Sequences and Their Applications. Volume XI: Censorship Under Weak Dependence. K. Yoshihara.	Tokyo: Sanseido, 2000, pp. vii + 377.
Option Pricing and Portfolio Optimization, Modern Methods of Financial Mathematics.	R. Korn and E. Korn.
Operations Research: A Practical Introduction.	M.W. Carter and C.C. Price.
Sampling Methodologies with Applications.	P.S.R.S. Rao.
STATISTICAL PROCESS CONTROL IN INDUSTRY: IMPLEMENTATION AND ASSURANCE OF SPC. R.J.M.M. Does, K.C.B. Roes and A. Trip.	Dordrecht, The Netherlands: Kluwer, 1999, pp. xi + 231, DFL195.00/US$117.00/Ł69.00.
STATISTICAL MODELLING WITH QUANTILE FUNCTIONS.	W.G. Gilchrist.
Annotated readings in the history of statistics.	H.A. David and A.W.F. Edwards.
The Lady Tasting Tea. How Statistics Revolutionized Science in the Twentieth Century.	D. Salsburg.
The Subjectivity of Scientists and the Bayesian Approach.	S.J. Press and J.M. Tanur.
Mathematics of Chance.	J. Andel.
Encyclopedia of Epidemiological Methods.	M.B. Gail and J. Benichou.
An Introduction to randomized controlled clinical Trials.	J.N.S. Matthews
An Introduction to Probability and Statistics, 2nd edition.	V.K. Rohatgi and A.K.M.E. Saleh.
Statistical Methods in Spatial Epidemiology.	A.B. Lawson.
Handbook of Statistical Genetics.	D.J. Balding, M. Bishop and C. Cannings (Eds.).
Geostatistics for Environmental Scientists.	R. Webster and M.A. Oliver.
Block Designs. Volume 1: A Randomization Approach.	S. Kageyama and T. Calinski.
Finite Population sampling and inference. A Predictive Approach.	R. Valliant, A.H. Dorfman and R.M. Royall.
Cluster Analysis, 4th edition.	B.S. Everitt, S. Landau and M. Leese.
Applied Multivariate Data Analysis, 2nd edition.	B.S. Everitt and G. Dunn.
Bayesian Statistical Modelling.	P. Congdon.
Correlation and Dependence.	D.D. Mari and S. Kotz.
Likelihood Methods in Statistics.	T.A. Severini.
Probabilistic Risk Analysis: Foundations and Methods.	T. Bedford and R. Cooke.
Handbooks in Mathematical Finance. Option Pricing, Interest Rates and Risk Management.	E. Jouini, J. Cvitanić and M. Musiela (Eds.).
Continuous Stochastic Calculus with Applications to Finance.	M. Meyer.
Time Series Forecasting.	C. Chatfield.
Time Series Analysis by State Space Methods.	J. Durbin and S.J. Koopman.
The Estimation and Tracking of Frequency.	B.G. Quinn and E.J. Hannan.
Practical Forecasting for Managers.	J.C. Nash and M.M. Nash.
The Efficient Use of Quality Control Data.	K.W. Kemp.
Sequential Monte Carlo Methods in Practice.	A. Doucet, N. de Fretas and N. Gordon (Eds.).
Levy Processes: Theory and Applications.	O.E. Barndorff-Nielsen, T. Mikosch and S.I. Resnick (Eds.).
SUBSAMPLING.	D.N. Politis, J.P. Romano and M. Wolf.
ADAPTIVE REGRESSION.	Y. Dodge and J. Jureckova.
ROBUST DIAGNOSTIC REGRESSION ANALYSIS.	A. Atkinson and M. Riani.
PARAMETRIC STATISTICAL CHANGE POINT ANALYSIS.	J. Chen and A.K. Gupta.
Semi-Markov Processes and Reliability.	N. Limnios and G. Oprisan.
Stochastic Spectral Theory for Self-Adjoint Feller Operators: A Functional Integration Approach.	M. Demuth and J.A. van Casteren.
STATISTICAL PATTERN RECOGNITION.	A. Webb.
MODELLING SURVIVAL DATA: EXTENDING THE COX MODEL.	T.M. Therneau and P.M. Gambsch.
ANALYSIS OF MULTIVARIATE SURVIVAL DATA.	P. Hougaard.
METHODS FOR META-ANALYSIS IN MEDICAL RESEARCH.	A.J. Sutton, K.R. Abrams, D.R. Jones, T.A. Sheldon and F. Song.
COMPUTATIONAL MOLECULAR BIOLOGY: AN INTRODUCTION.	P. Clote and R. Backhofen.
STATISTICAL INFERENCE IN SCIENCE.	D.A. Sprott.
STOCHASTIC PROCESSES. INFERENCE THEORY.	M.M. Rao. Dordrecht,
ASYMPTOTICS IN STATISTICS. SOME BASIC CONCEPTS, 2nd edition.	L. Le Cam and G. Lo Yang.
ASYMPTOTIC THEORY OF STATISTICAL INFERENCE FOR TIME SERIES.	M. Taniguchi and Y Kakizawa.
MARKOV POINT PROCESSES AND THEIR APPLICATIONS.	M.N.M. van Lieshout.
COUPLING, STATIONARITY, AND REGENERATION.	H. Thorrison.
RUIN PROBABILITIES.	S. Asmussen.
DERIVATIVES IN FINANCIAL MARKETS WITH STOCHASTIC VOLATILITY.	J.P. Fouque, G. Papanicolaou and K.R. Sircar.
NONLINEAR TIME SERIES MODELS IN EMPIRICAL FINANCE.	P.H. Franses and D. van Dijk.
STOCHASTIC CALCULUS AND FINANCIAL APPLICATIONS.	J. Steele.

Contents:
PART I: Foundations: Linear Methods
1. Matrix algebra
2. Systems of linear equations
PART II: Foundations: Nonlinear Methods
3. Unconstrained maximization and minimization
4. Constrained maximization and minimization
PART III: Applications: Iterative Methods for Nonlinear Problems
5. Solving nonlinear equations
6. Solving unconstrained maximization and minimization problems
PART IV: Applications: Constrained Optimization in Linear Models
7. Linear programming: Fundamentals
8. Linear programming: Extensions
9. Linear programming: Interior point methods
PART V: Applications: Constrained Optimization in Nonlinear Models
10. Nonlinear programming: Fundamentals
11. Nonlinear programming: Duality and computational methods

A more appropriate title for this text would be "Optimization: Foundations and Algorithms"; applications only occur in the exercises. This is a modern book in that it covers linear and nonlinear programming and so is able to include a valuable section on Interior Point Methods. The material is presented in an informal fashion using, where possible, geometric interpretations to support the algebra. The algorithms are described in a well-blended mixture of algebraic and numerical examples. The author is concerned about neither mathematical proofs of convergence nor a practitioner's interest in when convergence will happen. The author's extensive teaching experience is reflected in his upbeat, relaxed writing style and presentation. Should you have to teach undergraduate optimization to non-mathematicians this book would be useful. At the end of each chapter there are references and problems. It is a pity that many of the recent survey books and articles are not included in the references.

Contents:
PART I: Collecting Data
1. School-based drug prevention: Challenges in designing and analyzing social experiments
2. The health insurance experiment: Design using the finite selection model
3. Counting the homeless: Sampling difficult populations
PART II: Defecting Effects
4. Periodicity in the global mean temperature series?
5. Racial bias in death sentencing: Assessing the statistical evidence
6. Malpractice and the impaired physician: An application of matching
PART III: Understanding Relationships
7. Supply delays for F-14 jet engine repair parts: Developing and applying effective data graphics
8. Hospital mortality rates: Comparing with adjustments for case mix and sample size
9. Eye-care supply and need: Confronting uncertainty
10. Modeling block grant formulas for substance abuse treatment

Readership: Advanced undergraduate and graduate students of statistics and/or public policy, and empirical researchers and policy makers (especially at government and other research institutes)

RAND is a research institute created by the U.S. Air Force originally with a mandate "to provide objective research on national security issues." It is now an independent research organization that through grants and contracts from a variety of sources provides a research resource for public policy makers. The RAND Statistics Group was formed in 1976 and this book is a collection of some of their case studies.
Authored by the statistical investigators, each chapter lays out a statistical case study in a common nine section format: Executive Summary, 1. Introduction (always comprised of A. Policy Problem, B. Research Questions, C. Statistical Questions, and D. Summary of Data and Methods), 2. Design, Data Collection, Description of Data Sources and Description of Data, 3. Datafile Creation, Destructive Stats and Exploratory Analysis, 4. Statistical Methods and Models, 5. Results, 6. Discussion (covering policy implications and statistical issues), 7. Exercises and finally further RAND Reading (accessible at www.rand.org ). The sets of data for each chapter and errata are available on the Web (www.rand.org/centers/stat/casebook).
As with any collection of papers, some chapters are better than others; as with any statistical investigation, different approaches might have been taken in each case. Rather than detract from the book, these make the book a more interesting resource to be enlivened by an instructor of an advanced undergraduate or graduate course in statistics. Students of public policy might find the statistical aspects of the case studies somewhat challenging.
I strongly recommend it as a resource to instructors in statistics. Its breadth of applications and its organization of topics within papers make the book an important contribution to the growing collection of books on case studies in statistics.

Contents:
1. How many sweets in the jar?
2. Loose change and tight packing
3. Hard problems with hard spheres
4. Proof positive?
5. Peas and pips
6. Enthusiastic admiration: The honeycomb
7. Toils and troubles with bubbles
8. The architecture of the world of atoms
9. Apollonius and concrete
10. The giant's causeway
11. Soccer balls, golf balls and buckyballs
12. Packing and kisses in high dimensions
13. Odds and ends
14. Conclusion

Readership: An entertaining introduction to the field for both specialists and the more general public

This book is packed with examples of 'packing' in mathematics, physics, biology and engineering. In 1998 a solution was claimed (by Thomas Hales) to the long-standing Kepler conjecture – that no arrangement of spheres of equal radius in three-dimensional space has density greater than that of the face-centred cubic packing.
This remarkable result would provide a resolution, where many previous attempts have been found wanting. The Kepler conjecture is, in fact, a particular part of the eighteenth of the famous twenty-three problems posed by David Hilbert in 1900 to guide mathematical research.
The style of this book is concise and informal, but the material which is included, together with key references, will enable the curious reader to follow up the conjecture in its historical context and a large number of related problems with extensive applications. This is an excellent read!

Contents:
1. Lucky infant – carefree child
2. Tragedies and triumphs
3. Earnest schoolboy
4. Academia
5. Senior undergraduate
6. Apprenticeship in research
7. Planning the future
8. Wireless signalling
9. The new physics
10. Natural alchemy
11. Consolidating a Nobel prize
12. The Nobel prize
13. Counting atoms
14. The atom unveiled
15. The world at war
16. Broadening research
17. Triumphal tour of home
18. Death and glory
19. Birth of the atom smashers
20. Elder statesman of science
21. Sundown

This book provides a comprehensive, scholarly and eminently readable account of the life of Ernest (Lord) Rutherford. He was born at Brightwater, New Zealand. The author traces Rutherford's school years at Foxhill, Havelock and Nelson College. From here he won a scholarship to Canterbury College, Christchurch, where he earned his first degree in 1892. Inspired by a colourful and controversial Professor Bickerton, he commenced research on a subject of his own choosing, the magnetization of iron at higher frequencies.
In 1895 he won an 1851 Scholarship with which he chose to work with Professor J.J. Thomson at the Cavendish Laboratory, Cambridge, England. There he began, work on the long distance detection of Hertzian waves and by 1896 had established a world distance record. At this point Thomson invited him to assist him in trying to understand electrical conduction in gases. When radioactivity was discovered a short time later, Rutherford utilized radioactivity which became his life's work.
Rutherford's appointment as Professor of Physics at McGill University, Montreal, brought him to Canada in 1898, and he continued his researches there until 1907. This book provides the first full study of his life and his work whilst in North America. His work was so successful that he was nominated for the Nobel prize in both Physics and Chemistry. He was awarded a Nobel prize in Chemistry in 1908 for demonstrating that radioactivity involves the natural transmutation of one atom species into another.
By this time Rutherford was Professor of Physics at the University of Manchester, England. He continued work on the scattering of á-particles and soon found that a very small number were scattered backwards. This led to the formulation of the nuclear model of the atom, a fundamental advance which should have justified the award of a Nobel prize in Physics. But in view of his earlier award, a second award was deemed unnecessary.
In 1919 he was appointed Cavendish Professor of Physics at Cambridge, succeeding Professor J.J. Thomson. The Cavendish Laboratory became the world centre for Physics and, under Rutherford's leadership, attracted such luminaries as Appleton, Blackett, Chadwick, Cockroft, Kapitza and Walton, all of whom won Nobel prizes. Rutherford died unfortunately in 1937 of a strangulated hernia. Being a Lord, protocol required that he be operated on by a titled doctor. The delay cost him his life.
This is a delightful book, full of anecdotes and quotations from original letters and documents. As one reads the book one can feel the state of development in science at every stage. It can be enjoyed by anyone, from high school student to research scientist.

Contents:
1. Origins, computer arithmetic and complexity
2. Symmetric-key cryptosystems
3. Public-key cryptosystems
4. Primality testing
5. Factoring
6. Advanced topics

Readership: Cryptography buffs from beginning undergraduate to research scientist

This is a great book! It can be used in many ways: for a university course at one extreme, and as selective light reading for pleasure at the other. The author's enthusiasm carries the reader along clearly and easily, spilling over to scores of fascinating, beautifully written footnotes, which include more than fifty mini-biographies. There are close to three hundred problems, half with solutions. The other half are available only in a solutions manual for the instructor; this, however, is a decision I deplore. Apart from that, this book is excellent and highly recommended.

Contents:
1. The role of statistics in environmental science
2. Environmental sampling
3. Models for data
4. Drawing conclusions from data
5. Environmental monitoring
6. Impact assessment
7. Assessing site reclamation
8. Time series analysis
9. Spatial data analysis
10. Censored data
11. Monte Carlo risk assessment
12. Final remarks
APPENDIX A: Some Basic Statistical Methods
APPENDIX B: Statistical Tables

This book is directed at environmentalists and those who have to make difficult and sometimes costly decisions about the environment. Such decisions should be based upon pertinent information, and much of that is statistical. This book aims to introduce the reader to statistical methods that are useful for this. Many of the methods described are standard, such as analysis of variance, multiple regression, simply repeated measures designs and time series. Other more specialized methods particularly suitable for this area, such as meta analysis, kriging for spatial data, point processes and censored data methods, are introduced. Although many numerical examples are given, the emphasis is upon creating an awareness of what methods are available rather than the acquisition of technical skill. Further information can be obtained from the extensive reference section.
Now that complex statistical models can be fitted with ease, challenges of appropriate data collection and interpretation still remain. This is especially true with environmental data which are mainly observational rather than experimental. Stress is laid on the importance of defining the sampling unit on the difference between true and pseudo-replication and on the formulation of appropriate null hypotheses. These topics, which have been the subject of much debate in the medicinal, pharmaceutical and ecological literature, receive scant attention in the mainstream statistical literature. The author pays special attention to the distinction between design-based inference where randomness is introduced by the manner in which the data are collected, and model-based inference where randomness is introduced by the model assumptions. On the whole he favours design-based inference and randomization tests of hypotheses.
This book will do much to promote good statistical practice in environmental matters, an area of worldwide concern.

Contents:
1. Introducing nonparametric methods
2. Centrality inference or single samples
3. Other single-sample inference
4. Methods for paired samples
5. Methods for two independent samples
6. Three or more samples
7. Correlation and concordance
8. Regression
9. Categorical data
10. Association in categorical data
11. Robust estimation

Readership: Statisticians, students of statistics, research workers, consultants

This is the third edition of a very good book on nonparametric statistics. It is a book for the practitioner, but it goes far beyond being a compendium of useful methods. It aims at promoting understanding as well. Good statistical practice is exemplified throughout. The results of each procedure are evaluated in terms of the power of the test and also interpreted in the context of the test study. Theoretical derivations are avoided, but the authors give insight by discussing simple numerical examples. Particularly commendable are their discussions of multiple comparisons and conditioning in the two by two contingency table.
Hypothesis testing has a central role in nonparametric inference. Improved software, StatXact in particular, has made exact p-values readily available. The authors use the p-value as a tool for weighing evidence against the null hypothesis rather than as the decision tool implicit in a fixed level of significance. This approach answers much of the criticism associated with over enthusiastic use of p-values. Attention too is given to interval estimation, which can be a difficult problem with nonparametric inference. In many cases, comparisons with asymptotic results and corresponding parametric methods are given.
Topics in the third edition include discussions of robust estimation, the bootstrap, angular data, capture recapture methods and the measurement of agreement between observers.
If I could only have one book on nonparametric methods, this would be my choice. It is highly recommended.

Contents:
1. Introduction
PART I
2. Getting started
3. The normal curve and outlier detection
4. Accuracy and inference
5. Hypothesis testing and small sample sizes
6. The bootstrap
7. A fundamental problem
PART II
8. Robust measures of location
9. Inferences about measures of location
10. Measures of association
11. Robust regression
12. Alternative strategies

This interesting book gives a very readable introduction about understanding basic statistics from the point of view of modern developments and insights achieved during the last forty years. The book has two parts. In Part I, which covers basic concepts, the aim is to provide a verbal and graphical explanation of why standard methods can be highly misleading and provides a framework for intuitively understanding the practical advantages of modern techniques. In Part II, the goal is to explain basic modern methods for dealing with the problems described in Part I to applied researchers.
This is an excellent book, which gives a thorough and very clear description of today's most important techniques of the basic standard methods with some historical background and special attention to keep the technical details to a minimum. The author has performed a real service to the profession. I enjoyed reading this book. However, I found a few minor typographical errors (e.g. pp. 56, 164), and there is a lack of complete references. The book is not only highly recommended, but it should be required reading for anyone embarking on a career as a statistician in any field where a critical evaluation of data is required.

Contents:
1. Introduction
2. Axioms of probability
3. Conditional probability and independence
4. Probabilities on a countable space
5. Random variables on a countable space
6. Construction of a probability measure
7. Construction of a probability measure on R
8. Random variables
9. Integration with respect to a probability measure
10. Independent random variables
11. Probability distributions on R
12. Probability distributions on Rπ
13. Characteristic functions
14. Properties of characteristic functions
15. Sums of independent random variables
16. Gaussian random variables (The normal and the multivariate normal distributions)
17. Convergence of random variables
18. Weak convergence
19. Weak convergence and characteristic functions
20. The laws of large numbers
21. The central limit theorem
22. L2 and Hilbert spaces
23. Conditional expectation
24. Martingales
25. Supermartingales and submartingales
26. Martingale inequalities
27. Martingale convergence theorems
28. The Randon-Nikodym theorem

Readership: Students at the graduate level needing a streamlined introduction to probability theory

The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically sound and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. The topics treated are those one would expect, except perhaps for the proof of Kolmogorov's strong law using backward martingales and a version of the martingale central limit theorem. Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience

Contents:
1. Introduction
2. Concentration inequalities
3. Uniform deviation inequalities
4. Combinatorial tools
5. Total variation
6. Choosing a density estimate
7. Skeleton estimates
8. The minimum distance estimate: Examples
9. The kernel density estimate
10. Additive estimates and data splitting
11. Bandwidth selection for kernel estimates
12. Multiparameter kernel estimates
13. Wavelet estimates
14. The transformed kernel estimate
15. Minimax theory
16. Choosing the kernel order
17. Bandwidth choice with superkernels

This book is built around a new look on the important problem of bandwidth selection in density estimation. This new method has been launched in two recent papers of the two authors in the Annals of Statistics. It is based on ideas of minimum distance methods and convergence theory for empirical measures, uniformly over certain classes. The method aims at finding estimators with universal properties that is valid for all (or nearly all) densities. The book is self-contained because a lot of fundamental inequalities and essential combinatorial techniques are collected in the first part of the book. There is a rich choice of exercises, some of which may be quite hard. This makes it interesting for classroom teaching. It is an attractive book that certainly provides inspiration for further research.

Contents:
1. Introduction
2. Morphometric data
3. Statistical models for landmark coordinate data
4. Statistical methods for comparisons of forms
5. The study of growth
6. Classification and clustering algorithms
7. Further applications of EDMA

The shape of a multivariate set of data is formally defined as a statistic that is maximally invariant under Euclidean motions and homotheties. Reflections are optional. Recent statistical work in the theory of random shapes has shed some light on new techniques for morphometrics using landmark based methods. In general terms, morphometrics can be defined as the quantitative study of shape and form. The idea that both shape and form statistics are maximal invariants has been around since the 1970s. Its incorporation into the morphometric literature, with its roots in D'Arcy Thompson's pioneering work on the growth and form, has been more recent.
The appearance of this book by Subhash Lele and Joan Richtsmeier is to be welcomed. In recent years there has been much discussion of the relative advantages of morphometric methodology developed by Fred Bookstein and his colleagues versus the EDMA approach advocated by Lele and Richtsmeier. Now readers can decide for themselves.

Contents:
1. The generalized lambda family of distributions
2. Fitting distributions and data with the GLD via the method of moments
3. The extended GLD system, the EGLD: fitting by the method of moments
4. A percentile based approach to fitting distributions and data with the GLD
5. GLD-2: the bivariate GLD distributions
6. The generalized bootstrap (GB) and Monte Carlo (MC) methods
Appendix A: Programs for Fitting GLD, GBD and GLD-2
Appendix B: Tables for GLD Fits
Appendix C: Tables for GBD Fits
Appendix D: Tables for GLD-2 Fits
Appendix E: Normal Distribution

Readership: Anyone who wants to fit a parameterized family to a distribution or to data

The GLD is a four-parameter distribution with a lot of flexibility. It can be fitted to a lot of distributions and a lot of sets of data. The basic method has various extensions and the authors are experts in the area. The presentation is careful and extensive but somewhat remorseless. The main text is 283 pages and these are followed by 154 pages of programs, tables, references and index. Each reference contains its page reference listings, a nice feature. This is a specialized book and it will be welcomed by the appropriate specialists.

Contents:
1. Notions of probability
2. Expectations of functions of random variables
3. Multivariate random variables
4. Functions of random variables and sampling distribution
5. Concepts of stochastic convergence
6. Sufficiency, completeness, and ancillarity
7. Point estimation
8. Tests of hypotheses
9. Confidence interval estimation
10. Bayesian methods
11. Likelihood ratio and other tests
12. Large-sample inference
13. Sample size determination: Two-stage procedures

Readership: Statistics or mathematics/statistics majors; first year graduate students in statistics or areas requiring
substantial understanding

A striking feature of this volume is the very large number of worked examples in the text, together with long sets of exercises and complements at the end of each chapter. This is an introductory text; no previous knowledge of probability or statistical theory is assumed, but a reasonably confident approach to mathematics seems desirable. The stated prerequisite is a year of calculus; the author considers this to be enough to understand a major portion of the book, but admits that "some familiarity with linear algebra, multiple integration and partial differentiation will be beneficial" for some sections of the book. Measure theory is neither required nor invoked. Mathematically, the general approach is reasonably rigorous; full proofs are given for a number of important results. In a pleasantly informal style, the author provides very helpful explanations and comments on the mathematical results throughout the book. This tutorial structure makes the book an excellent choice for self-study. In addition to a list of abbreviations and notation, and a few standard tables, the Appendix contains an unusual feature – brief biographical sketches of eighteen leading statisticians (including Fisher, Cramér, Kolmogorov, Neyman, Pearson, C.R. Rao, …). Many historical comments enliven the main text as well. There is a very useful bibliography of nearly three hundred entries. All this helps to make the book a handy reference as well as a good textbook.

Contents:
1. Introduction
2. Exponential smoothing
3. Stationary series
4. The state space approach
5. Fitting ARIMA models
6. The frequency domain and the spectrum
7. Estimation and use of power spectrum
8. Two or more series
9. The R language

The purpose of the book is to provide standard time series tools to a non-specialist with a reasonable background in mathematical statistics. The whole approach in the book is very informal, and the author took great care in explaining all necessary techniques in non-specialist terms without making it too technical. The standard topics, like identification, estimation and prediction associated with standard linear time series models, are covered. The author has provided time series routines in R which are freely available, and a website with sets of data from which any reader can download is also given. I found the book interesting and easy to understand. I believe the book will be useful to many who are interested in actual applications of time series and also to undergraduate and graduate students. I strongly recommend this book.

Content:
1. Introduction by D. Peńa and G.C. Tiao
PART I: Basic Concepts in Univariate Time Series
2. Univariate time series: Autocorrelation, linear prediction, spectrum, and state-space model by G.T. Wilson
3. Univariate autoregressive moving-average models by G.C. Tiao
4. Model fitting and checking, and the Kalman Filter by G.T. Wilson
5. Prediction and model selection by D. Peńa
6. Outliers, influential observations, and missing data by D. Peńa
7. Automatic modelling methods for univariate series by V. Gomez and A. Maravall
8. Seasonal adjustment and signal extraction in economic time series by V. Gomez and A. Maravall
PART II: Advanced Topics in Univariate Time Series
9. Heteroscedastic models by R.S. Tsay
10. Nonlinear time series models: Testing and applications by R.S. Tsay
11. Bayesian time series analysis by R.S. Tsay
12. Nonparametric time series analysis: Nonparametric regression, locally weighted regression, autoregression, and quantile regression by S. Heiler
13. Neural network models by K. Hornik and F. Leisch
PART III: Multivariate Time Series
14. Vector ARMA models by G.C. Tiao
15. Cointegration in the VAR model by S. Johansen
16. Identification of linear dynamic multi-input/multi-output systems by M. Deistler

Readership: Academic statistics teachers and researchers, statistics practitioners
in industry and government

The book is based on lectures given at ECAS '97 (European Courses in Advanced Statistics) in Spain in September 1997, the sixteen chapters being shared between eleven contributors. The stated object is to present an overview of the current status of time series research and practice. The three parts of the book, as listed in the contents, are concerned with basic univariate models and methodology, more modern approaches and multivariate techniques. A web site is given for downloading the data used in the book. The presentation, text, equations, diagrams, etc., is immaculate.
The material is thoroughly and carefully presented, with a list of references at the end of each chapter. The coverage of the subject is quite comprehensive, with most of the standard topics described and analyzed in some detail. There are a few omissions, such as long-range dependence and wavelets, but the book can be seen as a very useful addition to any collection both for learning and reference.

Contents:
1. Basic principles of experimentation
2. Basic statistical calculations
3. Basic data summary
4. The normal distribution, the t-distribution and confidence intervals
5. Introduction to hypothesis testing
6. Comparison of two independent sample means
7. Linear regression and correlation
8. Curve fitting
9. The completely randomised design
10. The randomised block design
11. The Latin square design
12. Factorial experiments
13. Comparison of treatment means
14. Checking the assumptions and transformation of data
15. Missing values and incomplete blocks
16. Split plot designs
17. Comparison of regression lines and analysis of covariance
18. Analysis of counts
19. Some non-parametric methods

Readership: Practical, particularly agricultural experimenters, plant and crop scientists, undergraduate students

This is an introductory text aimed at students who need to understand statistical analysis of designed experiments, particularly in the agricultural, plant and crop research environments. One of the stated objectives is to encourage students to review the underlying principles of many statistical tests before using them in their research. The text begins with a discussion of the basic ideas of random sampling using several practical sets of data. This is followed by chapters on simple statistical calculations used to summarize data with means and standard deviations. The normal distribution is described and used as the sampling distribution of the sample mean to determine confidence intervals, and the t-distribution is introduced to deal with the case where the standard deviation is estimated from normal samples. There is very little theoretical development, and mathematics is kept to a minimum. The material follows a very traditional 'service course', including tests of hypotheses, one and two sample t-tests, paired t-tests, simple linear regression and a short section on fitting particular non-linear models. Chapters 9 to 12 cover the design and analysis (ANOVA) of simple experiments from completely randomized designs to factorial experiments. The models are almost exclusively fixed effect models, although the term 'random effects' is mentioned briefly. Confounding and fractional replication in factorial experimentation receive very limited explanation. Multiple comparison procedures and treatment contrasts are covered in Chapter 13. Throughout the text the emphasis is on investigation of the assumptions underlying the methods, and later chapters deal with handling situations where the assumptions are violated using transformations or non-parametric methods. Many examples analyzed using Minitab, SAS or Genstat are included. The book could be suitable for a practical course to science students wishing to appreciate statistical methods in agricultural and environmental research.

Contents:
1. Introduction
2. One-way classifications
3. Single predictor regression
4. Linear models (LMs)
5. Generalized linear models (GLMs)
6. Linear mixed models (LMMs)
7. Longitudinal data
8. GLMMs
9. Prediction
10. Computing
11. Nonlinear models

Readership: Statistical modellers, applied statisticians, industrial practitioners

This text is to be highly recommended as one that provides a modern perspective on fitting models to data. The emphasis is on the use of maximum likelihood (ML) and restricted maximum likelihood (REML) to fit linear, generalized and mixed models. A complete development of the theory is provided in each case, and there are many practical examples used to illustrate the methodology. The book begins with a review of basic linear models and linear mixed models, then moves on to describe generalized linear models, generalized mixed models and some non-linear models. The models get progressively more difficult, but the use of ML and REML provides a unified approach that extends readily to models based on non-normal distributions such as the Poisson or binomial. The main concepts, including fixed and random effects with both normal and binomial data, are introduced in the early chapter on one-way classification. Single predictor regression methods, including logistic regression, are described for linear and non-linear models with balanced and unbalanced data. These concepts are extended in greater generality and depth in later chapters which cover a variety of different models, linear models, generalized linear mixed models, leading eventually to chapters on handling longitudinal data with linear mixed models, on linear prediction and on the computational issues involved in obtaining ML estimates using the EM algorithm, numerical quadrature and Markov chain Monte Carlo methods. The development relies heavily on matrix algebra and many assumed statistical results with most of these provided in two detailed appendices. The first few chapters would form a graduate level course on modern modelling methods, while the later chapters will provide much useful research material.

Contents:
1. An introduction to general linear models: Regression, analysis of variance and analysis of covariance
2. Traditional and GLM approaches to independent measures single factor ANOVA designs
3. GLM approaches to independent measures factorial ANOVA designs
4. GLM approaches to repeated measures designs
5. GLM approaches to factorial measures designs
6. The GLM approach to ANCOVA
7. Assumptions underlying ANOVA, traditional ANCOVA and GLMs
8. Some alternatives to traditional ANCOVA
9. Further issues in ANOVA and ANCOVA

Readership: Undergraduate and postgraduate students reading behavioural science, education, psychology or social science

Regression techniques and the analysis of (co-)variance (ANOVA/ANCOVA) are probably the most frequently applied of all statistical techniques. Historically, regression and ANOVA developed in different research areas and addressed different questions. Consequently, separate analysis traditions evolved and encouraged the mistaken belief that regression and ANOVA constituted fundamentally different types of statistical analysis. When regression, ANOVA and ANCOVA are expressed in matrix algebra terms, a commonality is evident – this common pattern is the general linear model (the GLM in the title). This text is written to introduce GLMs and, consequently, the book is aimed primarily at the beginning researcher who needs to know how to use the particular techniques presented. It is acknowledged that many readers will not be well-versed in matrix algebra, so scalar algebra and textual descriptions are employed to facilitate comprehension. The text makes little reference to statistical packages, but the author briefly mentions commercially available statistical packages offering GLM programmes. Finally, for the targeted audience, the text will make a valuable addition to any library but, once read, is unlikely to become a reference source.

Contents:
PART I: I Need To Do Regression Tomorrow
1. Building models with regression and correlation
2. More than one independent variable – multiple regression
3. Categorical independent variables
PART II: I Need To Do Regression Analysis Next Week
4. Assumptions in regression analysis
5. Issues in regression analysis
PART III: I Need To Know More of the Things that Regression Can Do
6. Non-linear and logistic regression
7. Moderator and mediator analysis
8. Introducing some advanced techniques: Multilevel modeling and structural equation modeling
APPENDIX 1: Equations
APPENDIX 2: Doing Regression with SPSS
APPENDIX 3: Statistical Tables

This is a beginner's book for psychologists, written by psychologists, "even though it may have the appearance of being about statistics (Preface)." It provides basic commonsense comments and reads well but has little depth regressionwise. The algebra is minimal, the computing is reduced to following SPSS screen photos and there are no exercises. Nevertheless, it serves the purpose of getting psychologists acquainted with regression using a friendly, conversational format.

Contents:
1. Introduction to the logistic regression model
2. Multiple logistic regression
3. Interpretation of the fitted logistic regression model
4. Model-building strategies and methods for logistic regression
5. Assessing the fit of the model
6. Application of logistic regression with different sampling models
7. Logistic regression for matched case-control studies
8. Special topics

Readership: Graduate students in biostatistics and epidemiology, applied statisticians

In the ten years since the first edition of this book [Short Book Reviews, Vol. 10, p. 27], there has been continued research on all statistical aspects of the logistic regression model, together with improvements in the computer software necessary to carry out analyses. Amongst the topics that have been added to this revised edition are: new techniques for model building; an expanded discussion of assessing model performance; and new sections dealing with logistic regression models for multinominal, ordinal and correlated response data, exact methods and sample size issues. Statistical concepts are presented heuristically whenever possible, and mathe–matical details are kept to a minimum. The extensive sets of data discussed and analyzed in the text are available over the Internet via the World Wide Web rather than incorporated in the text as were the data listings included in appendices to the first edition. As in the first edition, the revised text continues to provide a focused introduction to the logistic regression model and its use in methods for modelling the relationship between a dependent categorical variable and a set of covariates.

Contents:
1. Introduction
2. Metric multidimensional scaling
3. Nonmetric multidimensional scaling
4. Further aspects of multidimensional scaling
5. Procrustes analysis
6. Monkeys, whisky and other applications
7. Biplots
8. Unfolding
9. Correspondence analysis
10. Individual differences models
11. ALSCAL, SMACOF and Gifi
12. Further m-mode, n-way models
APPENDIX: Computer Programs for Multidimensional Scaling

Readership: People who wish to apply multidimensional scaling methods in practice, or who need an introduction to the subject

The first edition of this book appeared in 1994. Additional material includes a new chapter on biplots, a discussion of the Gifi approach to nonlinear multivariate analysis and further computer programs. The volume comes with a CD-ROM containing DOS programs, and there is also a discussion of other multidimensional scaling (MDS) software.
MDS methods were originally developed by psychometric researchers, but are now widely used in areas which have included management, marketing, ecology, biology and human computer interaction. Their primary use is as a way of displaying data in a manner which can be conveniently assimilated by the human eye, though they also lead to more formal procedures for defining measurement scales.
The book will provide a good overview of the subject for people who hope to use MDS methods, and will also serve as an introduction to those who wish to explore the methods in more depth.

Contents:
1. Decision theory: An overview
2. Axiomatic bases of decision theory
3. Problem structuring, parameters and attributes
4. Group decisions and export judgement
5. Classical statistical decision theory
6. Bayesian statistical decision theory
7. Decision theory computations
8. Sensitive analysis
9. Sequential statistical decision theory
10. Conclusions

This ninth volume in Kendall's Library of Statistics surveys a half-century or more of contributions to both Bayesian and Wald decision theory. The result, in the authors' own words, is an "overview of the main ideas and concepts of statistical decision theory."
The book is modern in outlook and addresses such things as "belief nets", "group decision theory" and Monte Carlo methods of integration. At the same time, classical topics are studied, and a whole chapter is devoted to axiomatic foundations. Inevitably, individual topics must be given, at most, brief coverage. Thus, for example, "invariance" is covered in just three pages. Therefore, readers interested in such topics will need to go to one of the more than four hundred references included in the bibliography for a deeper understanding. In general, this will be a welcome and useful reference book. However, it does not have exercises and would not be suitable for use as a textbook.

Contents:
1. Structural equation modeling: An introduction to its history and current practice
2. Path analysis: Modeling systems of structural equations among observed variables
3. Factor analysis
4. Structural equation models in single and multiple groups
5. Statistical assumptions underlying structural equation modeling
6. Evaluating and modifying equation models
7. Multilevel structural equation modeling
8. Latent growth curve modeling
9. Epilogue: Toward a new approach to structural equation modeling and directions for future research

Readership: Graduate students in social and behavioural sciences, applied statisticians

Structural equation modelling (SEM) represents the hybrid of two separate statistical traditions – factor analysis developed within psychometrics, and the simultaneous equation modelling developed within econometrics. Most of the books discussing SEM concentrate on the practical aspects of the technique and are often nothing more than extended manuals of specific SEM software packages. This text, however, provides a general overview of the theoretical aspects of SEM, a solid discussion of likelihood-based inference for SEM and explains many of the most recent developments in structural equation modelling applied to complex sampling (multi-level SEM and latent variable growth). The reader is assumed to have a good background in statistics that includes multivariate analysis (factor analysis and path analysis) and matrix algebra. Familiarity with, or access to, one of the currently available software packages in SEM would be desirable in order to gain most from the text. SEM is not without its critics principally because it can easily be, and has frequently been, misused. The advanced treatment of SEM presented in this book should, I hope, help to reduce future misuse of the approach.

Contents:
1. Introduction
2. Algebraic models
3. Gröbner bases in experimental design
4. Two level factors: logic, reliability, design
5. Probability
6. Statistical modeling

This very challenging monograph demonstrates how Gröbner bases may be used to represent experimental designs, probability models and statistical models. The approach is illustrated with examples involving random variables with few points of support. Casting these problems in an algebraic framework exposes the nature of derived quantities such as conditional expectation. The book points clearly to the future potential use of algebraic tools.

Contents:
1. Introduction to wavelets
2. Review of Fourier theory and filters
3. Orthonormal transforms of time series
4. The discrete wavelet transform
5. The maximal overlap discrete wavelet transform
6. The discrete wavelet packet transform
7. Random variable and stochastic processes
8. The wavelet variance
9. Analysis and synthesis of long memory processes
10. Wavelet based signal estimation
11. Wavelet analysis of finite energy signals

The authors give a detailed survey of various wavelet methods in Chapters 2 to 6. The remaining chapters are devoted to the applications. The estimation of spectral density function, analysis of long memory processes and the estimation of signals in the presence of correlated noise have also been considered. Students should benefit from the exercises provided at the end of each chapter. This book, together with a recent book by B. Vidakovic (1999), Statistical modelling by Wavelets [Short Book Reviews, Vol. 20, p. 11], provides the readers with a comprehensive methodology. In my opinion the book by Percival and Walden should be available in every university library, and every time-series analyst must read this book for an alternative (to Fourier) set of techniques.

Contents:
PART I: Approximation, Bounds and Inequalities
1. Nonuniform bounds in probability approximations using Stein's method by L.H.Y. Chen
2. Probability inequalities for multivariate distributions with applications to statistics by J. Glaz
3. Applications of compound Poisson approximation by A.D. Barbour, O. Chryssaphinou and E. Vaggelatou
4. Compound Poisson approximations for sums of dependent random variables by M.V. Boutsikas and M.V. Koutras
5. Unified variance bounds and a Stein-type identity
by N. Papadatos and V. Papathanasiou
6. Probability inequalities for U-statistics by T.C. Christofides
PART II: Probability and Stochastic Processes
7. Theory and applications of decoupling by V. de la Pena and T.L. Lai
8. A note on the probability of rapid extinction of alleles in a Wright-Fisher process by F. Papangelou
9. Stochastic integral functionals in an asymptotic split state space by V.S. Korolyuk and N. Limnios
10. Busy periods for some queues with deterministic interarrival or service times by C. Lefevre and P. Picard
11. The evolution of population structure of the perturbed non-homogeneous semi-Markov systems by P. C.G. Vassilious and H. Tsakiridou
PART III: Distributions, Characterizations, and Applications
12. Characterizations of some exponential families based on survival distributions and moments by M. Albassam, C.R. Rao and D.N. Shanbhag
13. Bivariate distributions compatible or nearly compatible with given conditional information by B.C. Arnold, E. Castillo and J.M. Sarabia
14. A characterization of a distribution arising from absorption sampling by A.W. Kemp
15. Refinements of inequalities for symmetric functions by I. Olkin
16. General occupancy distributions by C.A. Charalambides
17. A skew t distribution by M.C. Jones
18. On the posterior moments for truncation parameter distributions and identifiability by posterior mean for exponential distribution with location parameters by Y. Ma and N. Balakrishnan
19. Distributions of random volumes without using integral geometry techniques by A.M. Mathai
PART IV: Time Series, Linear, and Non-Linear Models
20. Cointegration of economic time series by T.W. Anderson
21. On some power properties of goodness-of-fit tests in time series analysis by E. Paparoditis
22. Linear constraints on a linear model by S.D. Gupta
23. M-methods in generalized nonlinear models by A.I. Sanhueza and P.K. Sen
PART V: Inference and Applications
24. Extensions of a variation of the isoperimetric problem by H. Chernoff
25. On finding a single positive unit in group testing by M. Sobel
26. Testing hypotheses on variances in the presence of correlations by A.M. Mathai and P.G. Moschopoulos
27. Estimating the smallest scale parameter: Universal domination results by S. Kourouklis
28. On sensitivity of exponential rate of convergence for the maximum likelihood estimator by J.C. Fu
29. A closer look at weighted likelihood in the context of mixtures by M. Markatou
30. On nonparametric function estimation with infinite-order flat-top kernels by D.N. Politis
31. Multipolishing large two-way tables by K. Basford, S. Morgenthaler and J.W. Tukey
32. On distances and measures of information: A case of diversity by T. Papaioannou
33. Representation formulae for probabilities of correct classification by W.-D. Richter
34. Estimation of cycling effect on reliability by V. Bagdonavicius and M. Nikulin
PART VI: Applications to Biology and Medicine
35. A new test for treatment vs. control in an ordered 2x3 contingency table by A. Cohen and H.B. Sackrowitz
36. An experimental study of the occurrence times of rare species by M.F. Neuts
37. A distribution functional arising in epidemic control by N.G. Becker and S. Utev
38. Birth and death urn for ternary outcomes: Stochastic processes applied to urn models by A. Ivanova and N. Flournoy

Readership: Probabilists, statisticians, scientists working with statistical modeling

There are fifty-eight contributors to this volume. The thirty-eight papers were associated with the conference in honour of Professor Theophiles Cacoullos, which was held at the University of Athens, Greece in June 1999
In the preface, the editors write: "This volume has been put together in order to (i) review some of the recent developments in statistical science, (ii) highlight some of the new noteworthy results and illustrate their applications, and (iii) point out possible new directions to pursue."
Part I of this volume contains six articles on approximations, bounds and inequalities; Part II contains five papers on probability and stochastic processes; Part III discusses eight papers on distributions, characterizations and applications; Part IV discusses four papers on time series, linear and non-linear models; Part V includes eleven papers on inference and applications and Part VI is devoted to applications to biology and medicine with four papers.
Beyond minor typographical errors, as with any collection, the chapters differ in depth and complexity. However, the book contains some chapters of interest for probabilists and theoretical and applied statisticians. Most of the articles end with a complete list of references of recent developments, which will make it easier for graduate students and researchers in finding articles of interest.

Contents:
1. Uncertainty, intuition, and expectation
2. Expectation
3. Probability
4. Some basic models
5. Conditioning
6. Applications of the independence concept
7. The two basic limit theorems
8. Continuous random variables and their transformations
9. Markov processes in discrete time
10. Markov processes in continuous time
11. Action optimization: Dynamic programming
12. Optimal resource allocation
13. Finance: 'Risk-Free' trading and option pricing
14. Second-order theory
15. Consistency and extension: The finite-dimensional case
16. Stochastic convergence
17. Martingales
18. Large-deviation theory
19. Extension: Examples of the infinite-dimensional case
20. Quantum mechanics

Readership: Students with a basic mathematical faculty, interested in probability

The fourth edition still honours the statement made in the Preface to the 1982 Russian Edition: "When this text was published in 1970 I was aware of its unorthodoxy, and uncertain of its reception. Nevertheless, I was resolved to let it speak for itself, and not to advocate further the case there presented." The four editions have indeed spoken out loudly: a clear success in its unorthodoxy, Probability via Expectation has become a treasured classic. My 1976 edition has 239 pages; the over 100 extra pages in this edition are mainly due to various applications of probability theory, including chapters on dynamic programming, optimal resource allocation, option pricing and large-deviation theory. The different axiomatic approach (concentrating first on expectation and only later on probabilities) may for many still seem difficult to swallow in a world where Kolmogorov's triplet is so omnipresent. The dedicated reader should not shy away from this: even thirty years after its first appearance, the approach advocated still has its freshness and intellectual appeal. The applications discussed are interesting to whatever approach one adheres.

Contents:
1. Measures
2. Measurable functions and convergence
3. Integration
4. Derivatives via signed measures
5. Measures and processes on products
6. General topology and Hilbert space
7. Distribution and quantile functions
8. Independence and conditional distributions
9. Special distributions
10. WLLN, SLLN, and series
11. Convergence in distribution
12. Brownian motion and empirical processes
13. Characteristic functions
14. CLTs via characteristic functions
15. Infinitely divisible and stable distributions
16. Asymptotics via empirical processes
17. Asymptotics via Stein's approach
18. Martingales
19. Convergence in law on metric spaces
APPENDIX A: Distribution Summaries

Readership: Faculty, researchers and postgraduate students interested in mathematical statistics

This book offers a rigorous introduction to measure-theoretic probability with particular attention to topics of interest to mathematical statisticians. There is an unusual coverage with more attention to those probabilistic results used in mathematical statistics and asymptotics, including properties of the quantile and the empirical process, L- and R-statistics, U-statistics, the bootstrap and Skorokhod embedding. The style is mathematical while liberally interspersed with parenthetical remarks (e.g. "Nice!", "Everything else is even more trivial") and acronyms, even in chapter headings. This goes well beyond the traditional results in a first course in probability including Stein's approach on the Central Limit Theorem and is recommended for anyone interested in the probability underlying modern statistics.

Contents:
PART I: Fundamental Quality Improvement and Statistical Concepts
1. Introduction
2. Basic tools for improving quality
3. Basic concepts in statistics and probability
PART II: Control Charts and Process Capability
4. Control charts for measurements with subgrouping (for one variable)
5. Control charts for measurements without subgrouping (for one variable)
6. Control charts for attributes
7. Process capability
8. Alternatives to Shewhart charts
9. Multivariate control charts for measurement data
10. Miscellaneous control chart topics
PART III: Beyond Control Charts: Graphical and Statistical Methods
11. Other graphical methods
12. Linear regression
13. Design of experiments
14. Contributions of Genichi Taguchi and alternative approaches
15. Evolutionary operation
16. Analysis of means
17. Using combinations of quality improvement tools

Readership: Students in applied statistics and quality engineering; practicing statisticians and engineers in industry

This is a significant update of Professor Ryan's textbook from 1988. The chapters on statistical process control and process capability have been expanded considerably to include recent research in the field. The chapter on design of experiments is also longer, with the inclusion of robust design issues. The book is very well written.
While acknowledging the fashions of the day (Six Sigma in this edition, and "Japan's Approach" in the first edition), the author keeps his focus on the statistical issues that are at the heart of quality improvement. Most of the book is dedicated to control charting, process capability, and design of experiments – including Evolutionary Operation.
This book would be suitable for a second course for statistics students who are interested in a career in industry. Many references are provided, giving an up-to-date starting point for getting to know the literature.

Contents:
1. Introduction to reliability systems
2. Analysis and classification of reliability optimization models
3. Redundancy allocation by heuristic methods
4. Redundancy allocation by dynamic programming
5. Redundancy allocation by discrete optimization methods
6. Reliability optimization by non-linear programming
7. Metaheuristic algorithms for optimization in reliability systems
8. Reliability-redundancy allocation
9. Component assignment in reliability systems
10. Reliability systems with multiple objectives
11. Other methods for system-reliability optimization
12. Burn-in optimization under limited capacity
13. Case study on design for software reliability optimization
14. Case study on an optimal scheduled-maintenance policy
15. Case studies on reliability optimization
APPENDIX 1: Outline of Dynamic Programming
APPENDIX 2: The Hooke-Jeeves (H-J) Algorithm
APPENDIX 3: Derivation of Polytope U(k+1) from U(k)
APPENDIX 4: Consecutive k-out-of-n Systems

Readership: Academic (reliability engineering courses, statistics and operational research); industrial (reliability engineers
in manufacturing industries, e.g. electronics, automotive)

The book is a very wide-ranging and thorough treatise on the solution of difficult problems in reliability optimization. A huge field of work is covered on many and varied problems for which it is often extremely difficult to find practical solutions. The writing is clear and careful and reflects the pooled expertise of the four authors. I would recommend this book for both learning and reference.

Contents:
1. Terminology and notation for repairable systems
2. Probabilistic models: The Poisson process
3. Probabilistic models: Renewal and other processes
4. Analyzing data from a single repairable system
5. Analyzing data from multiple systems

The first third of the book presents stochastic point processes in a theorem-proof style. Chapter 4 uses graphical methods to examine the intensity function for single repairable systems. It looks at estimation and inference for various intensity processes, together with methods and advice for examining goodness of fit. There is some coverage on standards. Multiple systems are dealt with in Chapter 5, testing for common parameters across the different systems or characterising them by some prior distribution.
Intended for engineers, quality managers and statisticians, this book could also be used for a graduate level course in reliability. There are exercises at the end of each chapter. The book gives a set of methods to be tried; I would have liked more guidance on the most useful approaches to data. Reference to other texts on reliability is patchy: Bain and Engelhart (1991; Short Book Reviews, Vol. 11, p. 43) is included but the classic Lawless (1982; Short Book Reviews, Vol. 2, p. 14) text is not, nor are the more practical texts of Crowder, Kimber, Smith and Sweeting (1991; Short Book Reviews, Vol. 12, p. 6) and Ansell and Phillips (1994; Short Book Reviews, Vol. 15, p. 26), both of which include sections on repairable systems. No link is made to the adaptation of Cox's (1972) survival models to repairable systems, as shown, for example, by Lawless (J.Amer.Statist.Soc., 1987).

Contents:
1. Introduction
2. Methodological tools
3. Statistical estimation of basic characteristics
4. Basic characteristics and digitization
5. Covariance and spectral density
6. Size distribution of spherical parts
7. Nonspherical particles of constant shape
8. Size-shape distribution of particles
9. Arrangement of objects
10. Single phase polyhedral microstructures
APPENDIX A: Characteristics of Geometric Objects
APPENDIX B: Software Utilities

Readership: Scientists working in materials science, statisticians interested in applications of spatial statistics

For statisticians, the book provides many examples of the application of stereology, point process theory and the theory of random sets to questions of practical interest, and suggests how these problems have driven past research and still pose unanswered questions. Comprehensive discussions of Wicksell's problem and of the relationship between x-ray and random set moments appear seldom in the statistics literature, but these topics are comprehensively presented here. For materials scientists, the book gives an introduction to the analysis of two-dimensional and three-dimensional microscopic images, organized by the form of the data and utilizing up-to-date statistical techniques. Subroutines (in C) for calculating statistics that are not generally found in statistics packages are given, and much detail is given to the practicalities of estimating from digitized data statistics that describe continuous surfaces. The references are comprehensive, pointing to the derivations and proofs that this book has no room to contain.

Contents:
1. Bayesian computational approaches to model selection by C. Andieu, A. Doucet, W.J. Fitzgerald and J.M. Perez
2. Sequential analysis of non-linear dynamic systems using particles and mixtures by N. Gordon, A. Marrs and D. Salmond
3. Stochastic, dynamic modelling and signal processing: Time variable and state dependent parameter estimation by P. Young
4. The use of generalised likelihood measures for uncertainty estimation in higher order models of environmental systems by K. Beven, J. Freer, B. Hankin and K. Schulz
5. Spatial statistics in environmental science by R.L. Smith
6. Useful lies: Dynamics from data by A. Mees
7. A modelling framework for the prices and times of trades made on the New York stock exchange by T.H. Rydberg and N. Shepherd
8. The sample autocorrelations of financial times series models by R.A. Davis and T. Mikosch
9. The many roads to time frequency by P. Flandrin
10. Multiple window time varying spectrum estimation by M. Bayram and R. Baraniuk
11. Multitaper analysis of nonstationary and non-linear time series data by D.J. Thomson
12. Signal and image denoising via wavelet threshholding: Orthogonal and biorthogonal, scalar and multiple wavelet transform by V. Strela and A. Walden
13. Wavestrapping timeseries: Adaptive wavelet-based bootstrapping by D.B. Percival, S. Sardy and A.C. Davison

This volume contains thirteen papers (including four from the editors) by authors who participated and presented at one or more workshops held at the Newton Institute, Cambridge, during July-December 1998, as a part of the excellent programme on non-linear signal processing organized by the four editors. There is a heavy emphasis on Bayesian methodology (especially MCMC techniques) in signal extraction, wavelet methods in denoising and decorrelation of signals (also applied to long memory processes). Of course readers should remember that decorrelation (by whatever means) does not achieve much if the signals are non-linear and hence nonGausian, and this was never pointed out either here or anywhere else in the literature. Nowhere in the volume are the terms nonlinearity and nonstationarity defined. This is rather surprising when this volume is meant to address these topics. The papers included clearly reflect the interest of the editors and their view of analyzing such signals, but others may have alternative ideas. I found some papers difficult to understand even though they are supposed to be review papers. Despite these small reservations, I have no doubt many readers will find this volume useful.

Contents:
1. Operators and functions
2. Generalities on difference equations
3. Nörlund sum: Part one
4. Nörlund sum: Part two
5. The first-order difference equation
6. The linear equation with constant coefficients
7. Linear difference equations with polynomial coefficients

Readership: Mathematicians, researchers and postgraduates interested in difference equation methods and in queues

This monograph presents the author's Nörlund sum generalization of the Nörlund integral; this gives a solution of the Äů F(ů)=ř(ů) which reduces, as ů>0, to a solution of the differential equation DF(ů)=ř(ů). The author also develops a U-operator method analogous to the Lie-Gröbner method for differential equations; it provides approximate solutions for functional equations of the form G(ř(z))–l(z)G(z)=m(z). The Milne-Thomson operators, đ and ń, are applied in the final chapter to linear difference equations with polynomial coefficients, giving solutions in terms of factorial series.
The power of the author's methods is demonstrated via certain queuing models. There is no attempt, however, to give a comprehensive coverage of work on difference equations arising from queues; for example, for the exact solution of the transient M/M/1 queue the reader is referred only to Saaty.
The exercises are for self-study and rarely relate to queues. I was disappointed that the sole mention of a q-difference equation is in one of them.

Contents:
1. A primer on Markov chain Monte Carlo by P.J. Green
2. Causal inference from graphical models by S.L. Lauritzen
3. State space and hidden Markov models by H.R. Künsch
4. Monte Carlo methods on genetic structures by E.A. Thompson
5. Renormalization of interacting diffusions by F. den Hollander
6. Stein's method for epidemic processes by G. Reinert

Readership: Researchers and research students seeking an introduction to modern statistical work in complex stochastic systems

This book contains revised versions of the main papers presented at the 4th Séminaire Européen de Statistique on 'Complex Stochastic Systems'. It is intended to be tutorial in style. I shall not attempt to review all of the chapters, but simply describe the first three. Chapter 1, on Markov chain Monte Carlo is 'a primer for (those) seeking to get started in some aspect of MCMC research'. The author makes clear that it is not aimed at those who wish to use standard software, but rather for those who wish to develop their own. Chapter 2 describes issues of causality, which have recently attracted renewed interest within the statistical community. The author points out that graphical models provide a convenient structure within which to discuss such concepts, and describe such models, beginning with the fundamental, but sometimes ignored, distinction between conditioning by intervention, and conditioning by observation. Chapter 3 describes hidden Markov models, which continue to have a major impact on modern statistics. The author illustrates the range of applications and also describes estimation methods.
One often has reservations about edited volumes, but this one is an excellent introduction to some of the most important tools of modern statistics.

1. Foundation
2. Order statistics under weak dependence
3. Asymptotic properties of K-M estimators
4. K-M integrals for censored dependent data
5. Nonparametric estimators of d.f.'s
6. M-estimators for hazard functions

This nicely edited book is Volume XI in a series by the same author. These books deal with classical topics like partial sums, order statistics, density estimation, bootstrap, etc. in the situation of weak dependence. The present volume deals with the analysis of survival data and more specifically with the celebrated Kaplan-Meier estimator for the survival function. Since the original paper in 1958, there have been numerous papers with properties, extensions, modifications, etc. The present book studies properties on the Kaplan-Meier estimator in the case where the underlying survival times are dependent (and subject to random right censorship). Also, recent papers on Kaplan-Meier integrals, density functions, hazard rates, etc. are reconsidered from the viewpoint of weak dependence. The book contains no real data examples but is rather an interesting collection of theoretical results.

Contents:
1. Frequently used notation
2. The mean-variance approach in a one-period model
3. The continuous-time market model
4. Option pricing
5. Pricing of exotic options and numerical algorithms
6. Optimal portfolios

Readership: Advanced undergraduates in mathematics and statistics, graduates in financial economics

The aim of the book is to introduce Itô calculus to solve problems in modern finance. Therefore, the authors forsake generality which is not needed in the applications. Instead, the authors' scope is to write a self-contained book where mathematical results are not simply cited, but the concepts are developed and complete proofs are given. This approach, together with the well chosen finance topics and examples, makes the book especially useful for students seeking a lively introduction to Itô calculus.

Contents:
1. Introduction to operations research
2. Linear programming
3. Network analysis
4. Integer programming
5. Nonlinear optimisation
6. Markov processes
7. Queuing models
8. Simulation
9. Decision analysis
10. Heuristic techniques in operations research

To quote the authors, 'This book is designed as an introductory text course in Operations Research.' The chapter on heuristics techniques is particularly welcome. The mathematical skills required are an understanding of calculus and matrix algebra notation. The practical components of this text that are associated with each chapter are a Guide to Software Tools, and some illustrative case studies. The software sections give brief descriptions of the most popular commercial products; however, no contact information, for example web site or e-mail address, is given. This reviewer finds it strange that the authors describe both the intricacies of the techniques and available software yet barely mention the user interface, for instance modelling languages in mathematical programming. The illustrative case studies are one page summaries of published applications; to fully understand the power of the techniques it is necessary for the user to read the original paper.

Contents:
1. Introduction
2. Simple random sampling: Estimation of means and totals
3. Simple random sampling: Related topics
4. Proportions, percentages, and counts
5. Stratification
6. Subpopulations
7. Cluster sampling
8. Sampling in two stages
9. Ratio and ratio estimators
10. Regression estimation
11. Nonresponse and remedies
12. Further topics

Readership: Students and practitioners with one or two courses in basic theoretical and applied statistical concepts

This book covers most of the commonly used methods in sample surveys as well as some recent developments. The level of the book is elementary. Appendices at the end of each chapter present some mathematical derivations of basic results. The notation used is sometimes not consistent (for example, Appendices A2 and A3 on the properties of random variables, and the notation for combinatorics). Numerical examples illustrate the algebraic formulae. Examples of case studies illustrating how the survey methods are used in more complicated situations would be beneficial. The book includes useful references for further study, especially for recent developments in survey sampling methods.

Introduction
1. SPC: A historical perspective
2. SPC as part of quality policy
3. Implementation plans for SPC
4. Introducing SPC with teams
5. The plan of action for introducing SPC
6. Principles of the Shewhart type of control charts
7. Designing control charts to support improvement
8. Control charts
9. Tools for solving problems
10. From control to assurance
11. Software for SPC
12. SPC competition and self-evaluation

Readership: Managers and engineers seeking guidance on how to initiate statistical process control in manufacturing

This book is a revised translation of the original Dutch work from 1996. It presents statistical process control (SPC) as a philosophy for operations management on the shop floor. The statistical methods employed are the standard, simple, well-established ones.
The work is more a prescription for management strategy than a statistical textbook. The authors offer a
plan of activities by which companies with no prior experience with SPC can get started, developed from their experiences with three Dutch companies. Examples are given of SPC in mass production, in low volume production, and in very low volume production. The main value of the book is in the direction it can offer to non-statistical managers who want to help introducing SPC, but the reader will need to take care to adapt the authors' recommendations to their own companies' cultures.
Statistics itself occupies less than half the book. Not much numeracy is expected of the reader, but there are occasional, surprising, excursions into statistical theory in this volume which presumably was aimed at managers. The book would be a useful companion to be read together with a more traditional SPC text.

Contents:
1. An overview
2. Describing a sample
3. Describing a population
4. Statistical foundations
5. Foundation distributions
6. Distributional model building
7. Future distributions
8. Identification
9. Estimation
10. Applications
11. Regression quantile models
12. Bivariate quantile distributions
13. A postscript
APPENDIX 1: Some Usefull Mathematical Results
APPENDIX 2: Further Studies in the Method of Maximum Likelihood
APPENDIX 3: Bivariate Transformations

From the book preface: "This book looks at statistical modelling from a different perspective." The book deals with the steps of the statistical modelling process, using quantile methods, as a tool for problem solving. In the first chapter, the author gives a very good overview of the subject covering an overall process of background construction, identification, estimation, validation and application to show "the wood for the trees". No attempt has been made to apply the recommended approaches to a real large set of data as a sample. The reason mentioned by the author (p. 167) is for the sake of saving space, but it would
have been worth while to have added some extra pages. Beyond minor typographical and some notational errors, the book is a good introduction to the subject and will serve statisticians, researchers, etc. in their modelling work. The researchers will undoubtedly gain a lot of knowledge and insight of the core modelling ideas and techniques by reading this book.
I enjoyed reading this book; it is well written, easy to read and it would be worth considering as a text for honour students or as a seminar course at a graduate level.

Contents:
1. The introduction of the concept of expectation (Pascal, 1654)
2. The first formal test of significance (Arbuthnott, 1710)
3. Coincidences and the method of inclusion and exclusion (Montmort, 1713; N. Bernoulli, 1713; deMoivre, 1718)
4. The determination of the accuracy of observations (Gauss, 1816)
5. The introduction of asymptotic relative efficiency (LaPlace, 1818)
6. The logistic growth curve (Verhulst, 1845)
7. Goodness-of-fit statistics (Abbe, 1863)
8. The distribution of the sample variance under normality (Helmert, 1876)
9. The random walk and its fractal limiting form (Venn, 1888)
10. Estimating a binomial parameter using the likelihood function (Thiele, 1889)
11. Yule's paradox ("Simpson's paradox") (Yule, 1903)
12. Beginnings of extreme-value theory (Bortkiewicz, 1922; von Mieses, 1923)
13. The evaluation of tournament outcomes (Zermelo, 1929)
14. The origin of confidence limits (Fisher, 1930)
APPENDIX A: English Translations of Papers and Book Extracts of Historical Interest (Bibliography)
APPENDIX B: First (?) Occurrence of Common Terms in Statistics and Probability

The preface tells us that "Interest in the history of statistics has grown substantially in recent years..." How can we tell? It is true that the number of historical publications has grown, but how many people actually read them and what do they get out of them? Do you really want to read today a translation of a paper that E. Zermelo wrote in German in 1929 about the playing strengths of chess players in a tournament? (The underexplained example in that article refers to the famous New York 1924 tournament; however, chess players may be puzzled about what we can learn from the relevant "playing strengths" given, since they mirror the tournament order exactly.) If at this point in the review you are becoming annoyed with the reviewer's apparent attitude and are saying impatiently, "Of course we should study this sort of history!", you will enjoy this book very much. H.A. David translated three articles from the original French, six articles from German, and one from Latin; A.W.F. Edwards translated one from French; and S.L. Lauritzen one from Danish. Five more articles are reproduced in their original English. Each article is introduced by an essay called "Comments on…"; these comments are informative, interesting and beautifully written, and contain numerous modern connected references. The production is first class. H.A. David has used parts from this book "in a short course on the history of statistics, recently, given at Iowa State University." The collection is fun to browse. Statistics history buffs and browsers should order this book immediately.

Contents:
1. The lady tasting tea (Fisher, Design of Experiments)
2. The skew distributions (Galton and Karl Pearson)
3. That dear Mr. Gosset (Student t, and both K. Pearson and Fisher)
4. Raking over the muck heap (Fisher at Rothamsted)
5. "Studies in crop variarion" (Anova and controlled randomisation)
6. "The hundred year flood" (Tippett and E.J. Gumbel)
7. Fisher Triumphant (The logic of Inductive Inference, 1934)
8. The dose that kills (Bliss and Probits)
9. The bell shaped curve (Lindeberg, Lévy, Höffding)
10. Testing the goodness of fit (Neyman)
11. Hypothesis testing (Neyman and E.S. Pearson)
12. The confidence trick (The AIDS epidemic and confidence sets)
13. The Bayesian heresy (Mosteller and Wallace, de Finetti and Savage)
14. The Mozart of mathematics (Kolmogoroff)
15. The worms eye view (F.N. David)
16. Doing away with parameters (Wilcoxon, Chernoff and Savage, Pitman)
17. When part is better than the whole (biased sampling; Mahalanobis)
18. Does smoking cause cancer? (Doll and Hill vs Fisher)
19. If you want the best person (Gertrude Cox)
20. Just a plain Texas farm boy (S.S. Wilks)
21. A genius in the family (I.J. Good)
22. The Picasso of statistics (J.W. Tukey)
23. Dealing with contamination (G.E.P. Box)
24. The man who remade industry (W. Edwards Deming)
25. Advice from the lady in black (S.V. Cunliffe)
26. The march of the martingales (Lévy, Aalen, Andersen, Gill, Olshen)
27. The intent to treat (Peto, Cox, Box, and Rubin)
28. The computer turns upon itself (Efron)
29. The idol with feet of clay (Kuhn)
Afterword, timeline

The parentheses are reviewer's additions, indicating topics discussed.
A very unusual book, containing many excellent accounts of statistics in practice. The preface and some other chapters discuss deep issues of statistical philosophy. A fair number of amusing errors, e.g. neither of the Guinness family's two peers was Lord Guinness. A most interesting read.

Contents:
1. Introduction
2. Selecting the scientists
3. Some well-known stories of extreme subjectivity
4. Stories of famous scientists
5. Subjectivity in science in modern times: The Bayesian approach
APPENDIX: References by Field of Application for Bayesian Statistical Science

Readership: Professional scientists and the general public with an interest in science, in scientists, and in the methods
that scientists use

This book describes the role of subjectivity and preconceptions in science, via a series of vignettes illustrating how famous scientists in history achieved their major advances. Chapter 3 briefly describes how Kepler, Mendel, Millikan, Burt and Mead allowed their preconceptions to influence the data they chose to use on which to base their conclusions (or how they distorted or manufactured data to match their preconceptions). Chapter 4 describes the work of Aristotle, Galileo, Harvey, Newton, Lavoisier, Von Humboldt, Faraday, Darwin, Pasteur, Freud, Curie and Einstein. Each of the sections in Chapter 4 is divided into a brief historical sketch, an outline of their scientific contribution, a list of their major works, and a discussion of the role of subjectivity in the work. Most of these people are now regarded as having made a major contribution, but some of them are now regarded as little better than examples of self-deception. It is interesting to have them all examined from the same perspective, in which their preconceptions drive their theoretical developments.
As far as the role of bias, preconceptions and subjectivity is concerned in science, this book is fascinating. However, in many of the cases it seems contrived to attach it to today's formal methods of Bayesian inference.

Contents:
Introduction
1. Probability
2. Random walk
3. Principle of reflection
4. Records
5. Problems that concern waiting
6. Problems that concern optimisation
7. Problems on calculating probability
8. Problems on calculating expectation
9. Problems on statistical methods
10. The LAD method
11. Probability in mathematics
12. Matrix games

Readership: All students of probability theory, applied statisticians in industry

This is a compilation of interesting and popular problems concerning mainly probability theory, with some statistics. The material is very accessible, in the most part requiring no more than basic elements of calculus. While there are many old favourites here, there are some novelties and some problems given a new slant through references to, for example, Olympiad problems and those which have appeared in the American Mathematical Monthly. The book is a translation and modification of the original Czech edition. There are some glitches as a result ('dice' as singular…), but most are not crucial. The problems inspire the reader to follow up references and the style is generally very engaging.
This is a very useful supplement to Problems and Snapshots from the World of Probability (Blom, Holst and Sandell – Springer-Verlag [1994; Short Book Reviews, Vol. 14, p. 22]) and the classic Fifty Challenging Problems in Probability (Mosteller – Addison Wesley, 1965, Dover, 1987).

This volume contains a selection of excellent articles on many of the concepts, methods and tools that researchers working in epidemiology require. It is difficult to judge whether the selected topics would satisfy all appetites, as the field is becoming richer and more diversified. However, when consulting this volume regularly over the last two months, while investigating new projects and supporting students' dissertations, I have always found comprehensive and clear overviews at hand.
All entries are linked to each other by web-style cross-referencing and are enriched by up-to-date, but also historical, references for more in-depth reading. Most of the contributions are also rich of valuable insights in the topic, although sometimes the "encyclopaedic" style becomes rigid and too many classifications and sub-classifications are offered, for instance with differing listings of types of bias.
The articles are written by experts based in North America, Europe, Australia, New Zealand and Japan. Hence there is a wide perspective on several of the topics, as well as some differences. Many of the methodological articles already appeared in the Encyclopedia of Biostatistics but others have been added to cover specific issues, such as "birth cohort studies" and "cancer registries", or to introduce emerging or expanding fields, such as "genetic epidemiology". Some large topics, like case-control studies, have several articles from different authors which are often linked-up by short enlightened entries from one of the editors.
There is no doubt that this Encyclopedia dedicated to methods in epidemiology is an invaluable tool for researchers involved in medical and public health research as it offers an excellent springboard for acquiring and strengthening practical and methodological tools.

Contents:
1. What is a randomized controlled trial?
2. Bias
3. How many patients do I need?
4. Methods of allocation
5. Assessment, blinding and placebos
6. Analysis of results
7. Monitoring accumulating data
8. Subgroups and multiple outcomes
9. Protocols and protocol deviations
10. Some special designs: Crossover, equivalence and clusters
11. Meta-analyses of clinical trials

Over recent decades, randomized controlled clinical trials have become established as the method used to assess new treatments if claims of the efficacy of a treatment are to find widespread acceptance. This book provides an introduction to the statistical methodology that underpins the randomized controlled trial. Administrative aspects of running a trial receive little emphasis in the text but there are many excellent books on clinical trial methodology that the interested reader may consult. Trials with binary outcomes are given less prominence in the text than might be expected from their prevalence in medical practice, and survival analysis is completely omitted. Sections in the text that contain more advanced material are clearly identified with an asterisk so that such material might be omitted on a first reading – thus allowing use of the text within courses to be tailored to the needs of the student audience. The text assumes no underlying medical background, is well written and easy to read.

Contents:
1. Probability
2. Random variables and their probability distributions
3. Moments and generating functions
4. Multiple random variables
5. Some special distributions
6. Limit theorems
7. Sample moments and their distributions
8. Parametric point estimation
9. Neyman-Pearson theory of testing of hypothesis
10. Some further results of hypothesis testing
11. Confidence estimation
12. General linear hypothesis
13. Nonparametric statistical inference

Readership: Students taking postgraduate or final year undergraduate courses in mathematics

The book consists of three parts namely: (a) the core of the probability; (b) foundations of statistical inference; and (c) Chapters 11 to 13 on special topics. There is a wealth of material and, although the topics are of a conventional nature, the discussions and special topics are unique. Most of the presentations give far more depth than one would expect in a text of this type. There are five hundred and fifty problems with three hundred and fifty worked examples and one hundred and fifty references included in this comprehensive textbook. The mathematical prerequisites to reading this book are that the students should have had basic courses in linear algebra, set theory and a good background in calculus. This text is for mathematics specialists and not recommended as a service textbook.

Contents:
PART I: The Nature of Spatial Epidemiology
PART II: Important Problems in Spatial Epidemiology

The author has been a major influence in the development of statistical methods in epidemiology, and has been the principal editor of one recent major volume of papers on disease mapping and spatial epidemiology (Disease Mapping and Risk Assessment for Public Health [noted, Short Book Reviews, Vol. 19, p. 52]), and co-author of an introductory text on disease mapping (An Introductory Guide to Disease Mapping, with F. Williams). The former of these possibly represents a more advanced text, with the emphasis on more sophisticated modelling and technical detail, whereas the latter contains some of the material included here presented at a somewhat more basic level. In comparison, this book aims to provide an intermediate level introduction to a subject that has recently attracted much interest in both public health and applied statistics. It is organized into two sections, the first a general introduction to the field of spatial epidemiology, comprising five chapters detailing basic applications, modelling approaches and statistical formulations, and the second comprising six chapters on specific classic problems of particular public health importance or statistical interest. The content of Part I is quite general, whereas the second is more statistically explicit. Finally, five appendices give technical details of the statistical and computational approaches used throughout the book. There is an extensive bibliography, and web links where relevant data and software may be obtained. The computational requirements associated with inference for spatial epidemiological models are often demanding. Much reliance is placed on Markov chain Monte Carlo (MCMC) methods, and especially as packages such as BUGS are available with specially written spatial analysis modules (GeoBUGS is soon to be available from the Imperial College developers: n.best@ic.ac.uk). Little discussion is given in this text to practical or theoretical MCMC issues, but the implication given here, that the models described are implementable in practice, is definitely a realistic assessment.
This book represents a good general introduction to spatial epidemiology, with material presented at an intermediate level that is possibly most suitable as a postgraduate-level text for statistically trained researchers. Overall, it may be a little advanced for non-statisticians, but in Part I at least, where formal statistical content is fairly minimal, it is still accessible to the non-specialist statistician. Part II is aimed more at the spatial epidemiologist, and represents many of the standard (and some apparently more contentious) views of statistical modelling in the field. I can therefore recommend the book to such a mixed audience.

Contents:
PART 1: Bioinformatics
PART 2: Population Genetics
PART 3: Evolutionary Genetics
PART 4: Genetic Epidemiology
PART 5: Animal and Plant Genetics
PART 6: Applications

Readership: This is a comprehensive research resource, perhaps aimed predominantly at statisticians and applied probabilists, but also for numerate biologists and geneticists, at post-graduate level and above

This magnificent book attempts to catalogue and introduce all aspects of modern statistical genetics in a series of thirty chapters contributed by major researchers in the field. Topics range from the fundamental aspects of evolutionary theory and classical statistical genetics, to modern statistical genetics and bioinformatics, such as protein structure prediction. There is certainly suitable material here for a researcher new to the field to gain a good grounding in statistical genetics (if not genetics), but also sufficient advanced material to merit the attention of those already familiar with the field. Specific chapters I found particularly interesting and stimulating were those by Solovyev on gene prediction, by Weir on forensics, and by Schork et al on pharmacogenetics. I also found the section on evolutionary genetics and phylogenetics particularly informative. The structure of the book is excellent, and I found the final general index (covering all chapters) invaluable. My only minor criticism of the book as a whole is that, although in the main chapters give sufficient general detail without unnecessary specifics, some chapters omitted information (or relevant references) that would be required in order to begin an analysis from scratch. However, overall, I can thoroughly recommend it.

Contents:
1. Introduction
2. Basic statistics
3. Prediction and interpolation
4. Characterizing spatial processes: The covariance and variogram
5. Estimating the variogram
6. Modelling the variogram
7. Spectral analysis
8. Local estimation or prediction: Kriging
9. Cross-correlation, coregionalization and cokriging
10. Disjunctive kriging

As the authors state, "Geostatistics is not easy"; but this well-written and thorough book must surely make the learning process easier for environmental scientists with some facility in mathematics – to perhaps just high-school (English A-Level) standard for much of the content. The book concentrates on modern techniques based on the variogram and kriging. Most of the detail in these techniques is illustrated by pertinent graphs, diagrams and illustrations, using a mixture of real and simulated data. This book should enjoy the same success as Statistical Methods in Soil and Land Resource Survey, its predecessor by the same authors.

Contents:
1. Introduction
2. Basic terminology and preliminaries
3. General block designs and their statistical properties
4. Balance and efficiency: Classification of notions
5. Nested block designs and the concept of resolvability

This is the first volume of two. It covers in five chapters the questions of randomization in incomplete block designs.
This highly mathematical discussion is appropriate reading for mathematical statisticians who are interested in the intricacies of design of experiments. It will not be of much help to the practitioner who just wants to know how to analyze a balanced incomplete design.
It is written by two distinguished researchers in the mathematical theory of experimental design. The mathematical treatment throughout is thorough and, at times, difficult and intricate. It contains a mass of information, and introduces the principles with a thoughtful discussion of the simple randomized design and randomized complete block designs in Chapter 1.
The authors write in their preface that "this monograph does not pretend to give an exhaustive exposition of the theory of experimental design within the randomization approach." The authors are too modest. It comes very close to being exhaustive and, as a result, some of the intended audience will find it hard and slow to read.
The reader will have to wait until the second volume appears to learn about the construction of block designs.

Contents:
1. Introduction to prediction theory
2. Prediction theory under the general linear model
3. Bias-robustness
4. Robustness and efficiency
5. Variance estimation
6. Stratified populations
7. Models with qualitative auxiliaries
8. Clustered populations
9. Robust variance estimation in two-stage cluster sampling
10. Alternative variance estimation methods
11. Special topics and open questions
APPENDIX A: Some Basic Tools
APPENDIX B: Datasets
APPENDIX C: S-PLUS Functions

Readership: Survey samplers, researchers in survey methods, theoretical and practical statisticians

This text brings together many years of research into the development of the model-based (predictive) approach to inference in sample surveys. The basic philosophy is that survey data can be thought of as realizations of random variables and that inference can be based on models constructed to reflect this random process. In this way, the unobserved population units are predicted from the observed data using fitted regression models or general linear models. Throughout the book, the authors compare the model-based approach with the more traditional design-based methods, illustrating many new ideas with extensive numerical examples supported by simulation studies. The sets of data (available by ftp) for several large surveys, used in many of the examples and exercises, are given in an appendix as are a number of S-PLUS routines for performing various sampling and estimation tasks.
The methods discussed are wide-ranging, including concepts of robustness (bias robust against model failure) and jackknife variance estimation, and the theory is extensively described using heavy matrix algebra with a liberal use of generalized inverses. The material is aimed at researchers in this new conceptually demanding approach to the design and analysis of surveys. The presentation is meticulous and the authors have been careful to explain these difficult ideas clearly. There are many questions left unanswered which will be a source of ideas for future research and development. A highly recommended book which is an essential read for all research workers in this area.

Contents:
1. An introduction to classification and clustering
2. Visualizing clusters
3. Measurement of proximity
4. Hierarchical clustering
5. Optimization clustering techniques
6. Finite mixture densities as models for cluster analysis
7. Miscellaneous clustering
8. Some final comments and guidelines
APPENDIX: Software for Cluster Analysis

This is the fourth edition of a popular text whose third edition appeared eight years ago [Short Book Reviews, Vol. 13, p. 20]. In this edition, the number of authors has increased by two, the number of pages by about seventy and the list of references by about three hundred. The text retains its basic original structure and lucidity but has been extensively revised. Chapter 2 is now much more directly aimed at pictorial representation of clusters rather than of general multivariate data, and the material in the next three chapters has been ordered in a more logical fashion. Additions include more examples in each chapter, a greater technical background to many of the methods, and description of techniques developed in the 1990s. The Appendix is much more comprehensive and detailed than before, and over one hundred and twenty of the references are to work that has appeared since 1992. These are all distinct enhancements, and this continues to be an excellent general introduction to an important and expanding topic.

Contents:
1. Multivariate data and multivariate statistics
2. Exploring multivariate data graphically
3. Principal components analysis
4. Correspondence analysis
5. Multidimensional scaling
6. Cluster analysis
7. The generalized linear model
8. Regression and the analysis of variance
9. Log-linear and logistic models for categorical multivariate data
10. Models for multivariate response variables
11. Discrimination, classification and pattern recognition
12. Exploratory factor analysis
13. Confirmatory factor analysis and covariance structure models

Readership: Experimental scientists, statisticians, undergraduate and master students

The intermediate-level text book introduces readers to a wide range of multivariate analysis techniques. The second edition includes new sections on correspondence analysis, neural networks and random effects for repeated measures. A casualty of breadth is depth, and omitted are topics such as, the detail of how non-metric scaling works, how one might fit random-effects models, and some of the possible problems with hierarchical cluster analysis. Mathematical development is not extensive, and confined to boxes and tables. Discussion sometimes presents opposing views of the utility of techniques, as for instance in the summary section on exploratory factor analysis. This book is well-structured, and very well-written, and is bound to be a valuable source of reference for scientists. The many examples are improved and extended in this edition, and are a particular strength. There are over sixty exercises, and about a third of these have solutions provided. Anyone who reads this book will gain a good overall grasp of the subject. However, in order to carry out analyses, they will need further knowledge. Appendix A lists main computer package web-sites.

Contents:
1. Introduction: The Bayesian method, its benefits and implementation
2. Standard distributions: Updating, inference and prediction
3. Models for association and classification
4. Normal linear regression, general linear models and log-linear models
5. Ensemble estimates: Hierarchical priors for pooling strength
6. Latent variables, mixture analysis and models for non response
7. Correlated data models
8. Multilevel models, multivariate analysis and longitudinal models
9. Life table and survival analysis
10. Bayesian estimation and model assessment

This book is an extremely ambitious and largely successful attempt to describe the current state of applied Bayesian statistical practice. Although some theoretical aspects of the Bayesian paradigm are included, the emphasis of the book is strongly on applications, and therefore is perhaps close in spirit to the book of Carlin and Louis (Bayes and Empirical Bayes Methods for Data Analysis [Short Book Reviews. Vol. 17, p. 2]). The scope of applications in this book is much broader than Carlin and Louis, however, having numerous examples from the biological, medical, physical and social sciences; it is suitable for researchers in any of these fields who are not necessarily statistically trained. The worked examples include conjugate analysis, classification, (generalized) linear models, hierarchical models, latent variables, mixtures, time series and spatial models, multivariate analysis, longitudinal data, and survival analysis. The only major topics that receive insufficient attention are Bayesian non- and semi-parametrics (Bayesian flexible modelling), and even these are covered to a degree. The computational requirements associated with inference for sophisticated Bayesian models are often demanding, and this book leans heavily on Markov chain Monte Carlo (MCMC) methods in general, and on the package WinBUGS in particular. It is a remarkable achievement to have carried out such a range of analyses on such a range of sets of data.
I found this book comprehensive and stimulating, and was thoroughly impressed with both the depth and range of the discussions it contains. Although there are more suitable texts for the study of Bayesian theory, and some of the more difficult or controversial aspects are downplayed, I can certainly recommend it as a useful resource describing the practice of Bayesian statistics.

Contents:
1. Notations and definitions
2. Correlation and dependence: An introspection
3. Concepts of dependence and stochastic ordering
4. Copulas
5. Farlie-Gumbel-Morgenstern models for dependence
6. Global versus local dependence between random variables

The word "copula" is immediately intriguing.
I turned to Chapter 6 which opens on p. 65: "A copula provides a uniform representation of a bivariate distribution F on the unit square. This result is due to Sklar (1959)... ." Puzzled, I looked in the index. "Copula 65, 112, 162, 184." Then to the preface: "… copula: a focussed expression of dependence between two (or several) random variables, totally stripped of any other characteristics." Then to p. 2 (not mentioned in the index!) "… a copula, that is the o.d.f. on the unit square with uniform marginals." This book is not easy to read. Chapter 2 provides a nice historical record of definitions of dependence and independence; this is interesting, but it is marred by scores of minor glitches which make the reader hesitate and then retrace his steps. Examples: "Correlation may briefly defined…" (p. 12): "Prompted by Reed's remarks, a well known American mathematical statistician, H.L. Rietz (1918) was the first, to the best of our knowledge, to study…" (p. 13); "… indication of a greater degree of independence than it actually exists…" (p. 16); "Reaction to Galton's discovery in France was very swift." (p. 23); forty years after Bravais in 1886,…" (p. 24); "C.R. Rao (1893), while reminiscing on the origin and development of the correlation coefficient,…" (p. 24); "in a most interesting, but perhaps somewhat misleading contribution,…" (p. 28): "The proof use simular arguments as the Hoeffding lemma." (p. 35); and so on. My complaints are not about misprints like 1893 (every book has these) but about the writing style, including heavy misuse of commas, which makes smooth reading difficult. Two additional difficulties occur. The "long dash" which sets off an inserted statement is set as a "short dash" meant to link words as on p. 11; and words are sometimes broken at the end of a line in a ridiculous way, for example: har-m (p. 11); detail-s (p. 22).
Overall, I applaud the book as a brave effort to set out in detail a topic that, although extensive in nature, is usually given short shrift. The book should serve as a useful reference and/or provide the basis for a challenging seminar course.

Contents:
1. Some basic contents
2. Large sample approximations
3. Likelihood
4. First-order asymptotic theory
5. Higher-order asymptotic theory
6. Asymptotic theory and conditional inference
7. The signed likelihood ratio statistic
8. Likelihood functions for a parameter of interest
9. The modified profile likelihood function

As the author states in the preface "the emphasis in this book is on the development of statistical methods and a description of the underlying theory rather than on the statement and proof of precise mathematical results". Potential readers are assumed to have a good knowledge of graduate-level statistical theory to quite a high standard. The book then provides an introduction to conditional likelihoods, Edgeworth expansion and saddlepoint approximations for regular distributions, plus a summary of recent results in the field. For statisticians who are not specialists in likelihood theory, it could perhaps be used as a reference work for the many results on particular distributions which it quotes – although the subject index is somewhat limited for such a purpose. Alternatively, it could be used as a wide-ranging introductory work for research students intending to specialize in some part of likelihood theory.

Contents:
PART I: Introduction
1. Probabilistic risk analysis
PART II: Theoretical Issues and Background
2. What is uncertainty?
3. Probabilistic methods
4. Statistical inference
5. Weibull analysis
PART III: System Analysis and Quantification
6. Fault and event trees
7. Fault trees – analysis
8. Dependent failures
9. Reliability data bases
10. Expert opinion
11. Human reliability
12. Software reliability
PART IV: Uncertainty Modeling and Risk Measurement
13. Decision theory
14. Influence diagrams and beliefs nets
15. Project risk management
16. Probabilistic inversion techniques for uncertainty analysis
17. Uncertainty analysis
18. Risk measurement and regulation

Readership: "Numerate readers who have taken a first university course in probability and statistics, and who are
interested in mastering the conceptual and mathematical foundations of probabilistic risk analysis."

Our technological society has an increasing awareness of risk in all its facets. Brought down to its basic building blocks, risk is about uncertainty in frequency as well as severity of particular events. Mainly using examples from the technology sector (space, nuclear, chemical), the authors build up the various methods and tools needed for a quantitative assessment of risk. The presentation is to the point, clear and perfectly high-lighted through well-chosen practical examples and exercises. Besides the more technical issues surrounding fault and event-tree analysis, attention is also given to softer issues like expert opinion and human reliability. The only glaring omission is the economics of risk analysis; decisions on risk are taken within the context of economic reality and hence the modelling of this part of the equation is important. No doubt in the years to come we will see a closer link between the more reliability-based approach to risk analysis and the more economic one currently in use throughout the financial industry. This merger would lead to a truly risk-management platform.
I am convinced that Probabilistic Risk Analysis will provide a key input for this convergence effort. I for once learned a lot from reading this book and wholeheartedly recommend it for its intended readership. It is the ideal text on which to base an undergraduate course.

Contents:
PART I: Option Pricing: Theory and Practice
PART II: Interest Rate Modelling
PART III: Risk Management and Hedging
PART IV: Utility Maximization

Readership: Doctoral students, researchers and practitioners who already have a good knowledge of mathematical
finance

This book consists of a collection of invited papers, by different authors, which review the current state of practice in different areas of mathematical finance. Each chapter is described as having the structure of a brief review of existing results, an outline of more recent results, and a discussion of outstanding problems, with suggestions for how these might be tackled, but obviously the chapters differ in the amount of weight they put on these different aspects. The book is not for beginners. The blurb describes it as a 'handbook' and 'comprehensive reference work', and it will certainly be a useful reference work for people undertaking research in the area. I have to say also that it has been beautifully produced.

Contents:
1. Martingale theory
2. Brownian motion
3. Stochastic integration
4. Application to finance

Readership: Those with a background knowledge of measure-theoretic probability and Hilbert spaces as well as an interest in stochastic calculus and finance

The purpose of this book is to provide a minimalist, rigorous development of the theory of stochastic calculus with a view to the valuation of derivative securities. The development, from discrete-time martingales through stochastic integration with respect to continuous semi-martingales and dynamic trading strategies, is largely standard, and the author has concentrated on the core necessary for a discussion of continuous time financial models. Though rigorous, the book is perhaps easier to follow than texts devoted exclusively to stochastic calculus such as that of Karatzas and Shreve [Short Book Reviews, Vol. 19, p. 9] without the amusing conversational style of Steele [Short Book Reviews, Vol. 21, p. 9]. The final chapter on applications to finance provides a nice succinct discussion of European options, interest rate swaps, caps and floors.

Contents:
1. Introduction
2. Basics of time-series analysis
3. Univariate time-series modelling
4. Univariate forecasting methods
5. Multivariate forecasting
6. A comparative assessment of forecasting methods
7. Calculating interval forecasts
8. Model uncertainty and forecast accuracy

Readership: Researchers and practitioners using forecasting methods in economics, government, operations research, industry, and commerce

This book is a review of forecasting methods based on the analysis of time-series in their time-domain modelling framework. Not included are methods especially developed for particular fields such as meteorology.
It is not a text-book; therefore fully worked-out examples are not a significant feature, and it is light on theoretical exposition, with few formulae and equations. After a very basic summary of time-series modelling procedures, we meet ARIMA modelling, Box-Jenkins, the Kalman filter, exponential smoothing. We have small sections on non-linear models: TAR (threshold autoregression), regime-switching, GARCH (for modelling changes in volatility), neural networks and chaotic series. This is followed by multivariate methods: transfer function models, vector ARMA models and co-integration. None of these have more than a page or so. The coverage of prediction intervals, model uncertainty and forecast accuracy address important questions not always given adequate discussion.
However, the value of this book is not its catalogue of methods, but the way it draws our attention to recent work, and the sections devoted to comparing the methods and making recommendations as to their merits and application. In this way it gives insights that might otherwise only be gained through constant attention to the literature.

Contents:
1. Introduction
2. Local level model
3. Linear Gaussian state space models
4. Filtering, smoothing and forecasting
5. Initialisation of filter and smoother
6. Further computational aspects
7. Maximum likelihood estimation
8. Bayesian analysis
9. Illustrations of the use of the linear Gaussian model
10. Non-Gaussian and nonlinear state-space models
11. Importance sampling
12. Analysis from a classical standpoint
13. Analysis from a Bayesian standpoint
14. Non-Gaussian and nonlinear illustrations

The first nine chapters – three-quarters of the text – are devoted to the linear Gaussian model. The state-space formulation is contrasted with the ARIMA models of Box and Jenkins, notably in the use of structural models to explain trend and seasonal effects. A state-space model inevitably takes the form of an imperfectly observed vector autoregression, so the Kalman filter figures prominently and is derived efficiently. To the tasks of Chapter 4 is added that of parameter estimation. The authors are unaware of the extensive theory of state-space methods in control and optimization, which would have indicated a much stronger development of some of their ideas, but their intuition keeps them on a sound track.
The non-Gaussian case is largely restricted to the case of a linear autoregression with a disturbance from the exponential family, and is dealt with by efficient simulation methods. Both sections present interesting examples of applications.

Contents:
1. Introduction
2. Statistical and probabilistic methods
3. The estimation of a fixed frequency
4. Techniques derived from ARMA modelling
5. Techniques based on phases and autocovariances
6. Estimation using Fourier coefficients
7. Tracking frequency in low SNR conditions

It is probably true to say that many statisticians rarely come across the need to accurately estimate sinusoidal frequencies, or determine how many there are, especially in a noisy environment. However, such problems are ubiquitous in areas such as physics and electrical engineering. This book is a timely study of the statistical methods which can be employed, and their properties, written by B. Quinn and the late T. Hannan, two of the most active and productive researchers in the field. The text gives many of the mathematical details, and perhaps some material would have been better collected in appendices or exercises to improve the readability; also the index is much too brief for such a detailed book. Nevertheless, the book is a valuable and detailed quality reference source, and the MATLAB code provided will be appreciated by practical scientists.

Contents:
1. Why forecasts?
2. Planning the forecasting tasks
3. Measuring how well forecasting goals are met: Part 1
4. Data search, gathering, documentation and management
5. Qualitative forecasting: Long-term
6. Semi-quantitative methods
7. Forecasting, risk, and strategy management
8. Measuring how well forecasting goals are met: Part 2
9. Preliminary data analysis and forecasting
10. The preliminary forecast: Concepts and examples
11. A strategy for performing forecasting data analysis
12. Forecasting trend and season I: Multiple regression
13. Forecasting trend and season II: Smoothing methods
14. Forecasting trend and season III: Time series decomposition
15. ARIMA and related models for forecasting
16. Using ARIMA models: Other issues and examples
17. Comparing and combining forecasts
18. Variations on the theme of seasonal adjustment
19. Mixed and extended models
20. Nonlinear regression modelling
21. Artificial neural networks
22. Building the forecast report

Readership: Students on business management courses, professional managers and administrators needing a practical guide to forecasting

The authors of this text have researched their ground thoroughly; I suspect through the wealth of experience they have gained by teaching forecasting at this level. The book is strongly rooted in practical experience and shrewdly expresses the benefits and shortfalls of the statistical techniques described. Minitab and Excel are used extensively throughout the book with extra references to tools that can be found on the internet. The book is also supported by a complementary website at www.arnoldpublishers.com/support/nash, which contains exercises and the sets of data used in the text. The main emphasis is on straightforward ideas than can be easily understood and used in the business environment. Advanced topics are covered and explained in a manner that is clear how these techniques can be put into use. This book would be a useful addition to libraries needing to provide relevant texts on forecasting.

Contents:
PART I: Statistical Concepts
1. Some aspects of statistical quality control
2. Small samples: Decisions and consequences
3. Distributions relevant to process and test control
4. Effective use of sampled data
PART II: Principles and Criteria of Statistical Quality Control
5. Principles and criteria of statistical quality control
6. Better control rules
PART III: Control Using Cumulative Sums
7. Really efficient use of test data

This is an accessible but very intelligent monograph on the statistics of the quality control. Chapter 1 to 4 can nearly stand on their own as a first course in mathematical statistics, while Chapters 5 to 7 develop the foundations of Shewhart and cusum charts. The monograph is not intended as a handbook for practitioners.
Quality control has always been a small sample problem with attendant risks of misjudging the populations being controlled, but the author is right to re-emphasize this point as the motivation for his monograph: That the use of quality control data must be efficient in the statistical sense so that maximum information can be obtained from any investment in sampling and measurement
The monograph is more mathematical than data analytical, but students will be well prepared to negotiate the abundance of empirical control rules they will encounter in later life should they choose to become practitioners.

Contents:
1. An introduction to sequential Monte Carlo methods
2. Particle filters – A theoretical perspective
3. Interacting particle filtering with discrete observations
4. Sequential Monte Carlo methods for optimal filtering
5. Deterministic and stochastic particle filters in state-space models
6. RESAMPLE-MOVE filtering with cross-model jumps
7. Improvement strategies for Monte Carlo particle filters
8. Approximating and maximising the likelihood for a general state-space model
9. Monte Carlo smoothing and self-organising state-space model
10. Combined parameter and state estimation in simulation-based filtering
11. A theoretical framework for sequential importance sampling with resampling
12. Improving regularised particle filters
13. Auxiliary variable based particle filters
14. Improved particle filters and smoothing
15. Posterior Cramer-Rao bounds for sequential estimation
16. Statistical models of visual shape and motion
17. Sequential Monte Carlo methods for neural networks
18. Sequential estimation of signals under model uncertainty
19. Particle filters for mobile robot localization
20. Self-organising time series model
21. Sampling in factored dynamic systems
22. In-situ ellipsometry solutions using sequential Monte Carlo
23. Manouvering target tracking using a multiple-model bootstrap filter
24. Rao-Blackwellized particle filtering for dynamic Bayesian networks
25. Particles and mixtures for tracking and guidance
26. Monte Carlo techniques for automated recognition

Contents:
1. A tutorial on Lévy processes
2. Distributional, pathwise, and structural results
3. Extensions and generalizations of Lévy processes
4. Applications in physics
5. Applications in finance
6. Numerical and statistical aspects

Readership: Students and researchers in stochastic processes (i.e. Lévy processes) and their applications

Over the last decade, in numerous fields of applications which traditionally used Brownian motion based modelling, non-Brownian models entered the field. One such class of processes concerns the so-called Lévy processes, i.e. processes with stationary and independent increments. Lévy based models allow for a more realistic (often heavy-tailed) modelling of the distribution of the increments. This volume presents a useful summary of some of the recent scientific developments concerning Lévy processes. Both introductory and more advanced articles are included. The interested researcher will get a good overview of 'where the action is', whereas students will find numerous interesting research topics to work on. The fields of applications can be deduced from the Contents. It is fair to say that the text is biased towards probabilistic aspects; only few papers treat actual data fitting. On the other hand, the field is vast and expanding quickly so that realistically only a biased snapshot can be expected. I am convinced that the text will contribute further to making stochastic models based on general Lévy processes even more popular. I, therefore, take pleasure in recommending this volume to all interested readers.

Contents:
PART I: Basic Theory
1. Bootstrap sampling distributions
2. Subsampling in the I.I.D. case
3. Subsampling for stationary time series
4. Subsampling for nonstationary time series
5. Subsampling for random fields
6. Subsampling marked point processes
7. Confidence sets for general parameters
PART II: Extensions, Practical Issues, and Applications
8. Subsampling with unknown convergence rate
9. Choice of block size
10. Extrapolation, interpolation, and higher order accuracy
11. Subsampling the mean with heavy tails
12. Subsampling the autoregressive parameter
13. Subsampling stock returns

On an intuitive level, the subsampling techniques are based on the assumption that a sample, which we exercise with, is a valid "image" of the original population/probability space. Believing in that, we can consider this sample as a finite "population" and forget about its origin. Instead of experimenting with the real population we resort to experimenting with the latter. All experiments/subsamplings (like jackknifing, bootstrapping, moving blocks bootstrapping, etc.) can be done on the computer at a relative low expense. Those experiments generate some statistics and the authors are mainly concerned with their asymptotic behaviour when the size of "real" sample increases infinitely. They describe assumptions which must be imposed on the original sampling (for instance, weak convergence of the empirical distribution to the original distribution) to guarantee the reasonable asymptotic behaviour of the statistics based on extensive experiments with a smaller world – the sample in our hands. The book is one of the most comprehensive texts in the subsampling realm and provides a solid background for researchers working the related areas of statistics.

Contents:
1. Prologue
2. Regression methods
3. Adaptive LAD+LS regression
4. Adaptive LAD+TLS regression
5. Adaptive LAD+ M-regression
6. Adaptive LS+TLS regression
7. Adaptive choice of trimming
8. Adaptive combination of tests
9. Computational aspects
10. Some asymptotic results
11. Epilogue

This book deals with nonstandard techniques of regression estimation. Starting with well-known methods for regression estimation such as the least squares (LS) method, trimmed least-squares (TLS) method, least-absolute deviation (LAD) method, and Huber's robust M-method, the authors concentrate on adaptive estimators which minimize loss-functions that are convex combinations of loss-functions of two corresponding estimators. The detailed analysis of methods, as well as numerical illustrations, are presented.

Contents
1. Some regression examples
2. Regression and the forward search
3. Regression
4. Transformations to normality
5. Nonlinear least squares
6. Generalized linear models

Readership: Regression practitioners, and students of regression with knowledge of matrix algebra

This very down-to-earth volume explores regression models via a "forward search" technique in which samples of increasing size are taken from the data, and plots are made to show off chosen characteristics. An initial fit uses a best-fitting, robustly estimated model chosen from fits to small subsets of the data. The subset size is increased by one (sometimes one fresh point is added, sometimes two are added and one leaves, and so on). The fitting continues until all data are included. For each best subset choice we thus have n residuals available and their loci, as subset size changes, can be plotted and examined. Other plots (for example, of R2, Cook's statistics, t-statistics) can also be made. Programming was done in GAUSS, and S-Plus functions have been developed. A web site provides programs and data, and is expected to grow. These methods provide additional analysis techniques for regression practitioners, and the book is a welcome addition to the literature.

Contents:
1. Preliminaries
2. Univariate normal model
3. Multivariate normal model
4. Regression models
5. Gamma model
6. Exponential model
7. Discrete models

Readership: Theoretical and applied statisticians, quality control engineers and economists as well as graduate students in statistics

The change-point problem can be considered one of the central problems of statistical inference linking together theory of estimation and testing hypotheses, frequentist and Bayesian approaches, fixed sample and sequential procedures and parametric and nonparametric methods. This book deals with three parametric methods for fixed sample change-point inference: likelihood ratio procedure, informational approach and Bayesian approach. All but the most basic models are carefully developed with detailed proofs of asymptotic null distributions, and illustrated by using a number of data sets. The binary segmentation procedure is used to reduce the general problem of detecting and localization of many change points to the case of a single change point. Although all results are based on asymptotic theory, no Monte-Carlo results comparing the small sample performance of the procedures are presented. The book would make ideal reading for anyone contemplating undertaking research in the area.

Contents:
1. Introduction to stochastic processes and the renewal process
2. Markov renewal processes
3. Semi-Markov processes
4. Countable state space Markov renewal and semi-renewal processes
5. Reliability of semi-Markov systems
6. Examples of reliability modelling
APPENDIX A: Measures and Probability
APPENDIX B: Laplace-Stieltjes Transform
APPENDIX C: Weak Convergence

Semi-Markov or Markov renewal processes are ideal for modelling random phenoma that move between a set of states like a Markov chain but where the transition times need not be assumed to be either constant or exponentially distributed. Because of this great flexibility, these processes are used for modelling in many subjects. The first two-thirds of this monograph provides a reasonably thorough and readable overview of these and their related processes. The essential review of renewal theory that is included in the first chapter is well done and should be widely useful. Overall, the substantial review materials of the early chapters make this book a recommended reference for probabilistic modellers in many areas of application.
The last third of the book is devoted to the concepts and applications of reliability theory. Included therein is a coherent presentation of the main concepts and definitions of reliability, including failure rates, coherent systems, maintainability and performability. With the aim of making the models tractable, several methods for computing the key probabilistic quantities that arise in the models are presented and compared. Several specific examples including repair and shock models are worked out along with a brief discussion of model simulations. The authors have included an extensive list of recent references that adds to the overall usefulness of the book.

Contents:
1. Basic assumptions of stochastic spectral analysis: Free Feller processes
2. Perturbations of free Feller processes
3. Proof of continuity and symmetry of Feynman-Kac operators
4. Resolvent and semigroup differences for Feller operators: Operator norms
5. Hilbert-Schmidt properties of resolvent and semigroup differences
6. Trace class properties of self-adjoint Feller operators
7. Convergence of resolvent differences
8. Spectral properties of self-adjoint Feller operators
APPENDIX A: Spectral Theory
APPENDIX B: Semigroup Theory
APPENDIX C: Markov Processes, Martingales and Stopping Times
APPENDIX D: Dirichlet Kernels, Harmonic Measures, Capacities
APPENDIX E: Dini's Lemma, Scheffé's Theorem, Monotone Class Theorem

In the classical Schrödinger equation, one has a differential operator – half the Laplacian plus a suitable (Kato) potential, V; the solution is expressed by the Feynman-Kac formula. How do things vary when the potential V varies? And how far can one generalize this?
The appropriate generalization is to the theory of Feller processes – in terms of their resolvents, semigroups, spectral properties etc. – when one compares their potentials. Typically, one is interested in a potential becoming singular on a small set. Various physical contexts produce problems of this type: Quantum theory, quantum field theory, atomic or solid-state physics, etc.
The authors give a very thorough and detailed account of results in this area, using a combination of probabilistic and analytic methods. Much useful information on the diverse background areas is contained in the appendices.

Contents:
1. Introduction to statistical pattern recognition
2. Estimation
3. Density estimation
4. Linear discriminant analysis
5. Nonlinear discriminant analysis – neural networks
6. Nonlinear discriminant analysis – statistical methods
7. Classification analysis
8. Feature selection and extraction
9. Clustering
10. Additional topics
APPENDIX A: Measures of Dissimilarity
APPENDIX B: Parameters Estimation
APPENDIX C: Linear Algebra
APPENDIX D: Data
APPENDIX E: Probability Theory

Readership: Graduate students; teachers; researchers and practitioners in engineering, statistics, computer science, information technology and the social sciences who need an up-to-date account of the topic

This book deals mainly with classifier design. It contains descriptions of many of the most useful of today's pattern processing techniques including many of the recent advances in nonparametric approaches to discrimination.
Chapters 2 to 9 study the problems of data transformation and supervised classification (discrimination) and unsupervised classification (clustering) procedures. These chapters end with the subsections: application studies, summary and discussion, recommendations, notes and references, and exercises. Chapter 10 briefly addresses the classifier performance assessment and the problems with data: mixed variables, outliers, missing values and unreliable labelling. The exercises at the ends of Chapters 2 to 10 vary from 'open book' questions to more lengthy computer projects. Most of the illustrative examples to help guide the reader through the techniques presented come from real-world applications studies. More than seven hundred references (including references published in 1999) are provided where further details on applications, comparative studies and theoretical developments may be obtained. Four appendices largely cover background material and material appropriate if the book is used as a text for a 'conversion course'. All chapters begin with a theoretical overview, and most relevant electronic contact addresses are provided. However, an overview and a brief evaluation of the software packages available could also be very interesting for the practitioners and the other targeted readers too.
In conclusion, the book indeed provides a comprehensive account of the most recent advances in statistical pattern recognition techniques with emphasis on methods and algorithms for discrimination and classification. It will be very useful as an informed and thought-provoking source of reference, as well as a text for lecture courses.

Contents
1. Introduction
2. Estimating the survival and hazard function
3. The Cox model
4. Residuals
5. Functional form
6. Testing proportional hazards
7. Influence
8. Multiple events per subject
9. Fraility models
10. Expected survival
APPENDIX A: Introduction to SAS and S-Plus
APPENDIX B: SAS Macros
APPENDIX C: S Functions
APPENDIX D: Data Sets
APPENDIX E: Test Data

Readership: Professional statisticians, statistical practitioners, graduate students of statistics

The Kaplan-Meier estimator and Cox's proportional hazards model are the standard techniques for handling censored survival data. Over recent years an alternative view, based on counting processes and martingale theory, has enabled these models to be extended to more complex situations such as non-proportional hazards, multiple outcomes, subject-specific or fraility models. These methods are mathematically sophisticated. The authors do not shirk the mathematics but the emphasis is on concepts, and above all, on showing how to fit the models to data with SAS or S-Plus.
Of course fragments of computer code are given, but this is not a black-box approach. The authors go far beyond this. They have laid out for us the wealth of their practical experience at all levels; the numerical aspects; computer algorithms; evaluation of different methods and connections between them; possible pitfalls; and interpretation of the results. Remarkable insights abound.
This book complements that of P. Hougaard [Short Book Reviews, Vol. 21, p. 6] by giving much detail on the actual fitting of the models discussed by him. It will serve two audiences: the busy practitioner who has not had time to catch up with martingale theory and counting processes and the graduate student who has just completed such a course and who needs to be introduced to the practicalities and judgements needed in data analysis. It is likely to become a well-thumbed copy on the statistician's desk and statistical practice will be the better for it.

Contents:
1. Introduction
2. Univariate survival data
3. Dependence structures
4. Bivariate dependent measures
5. Probability aspects of multi-state models
6. Statistical inference for multi-state models
7. Shared fraility models
8. Statistical inference for shared fraility models
9. Shared fraility models for recurrent events
10. Multivariate fraility models
11. Instantaneous and short term fraility models
12. Competing risks
13. Marginal and copula modeling
14. Multivariate non-parametric estimates
15. Summary

Readership: Statisticians, graduate students of statistics, research workers in survival analysis

Over the last decade there have been vast developments in methods for the analysis of survival data, especially when independence between survival times cannot be assumed. The author has brought these developments together in a book that is destined to become the professional statistician's reference and the standard text for a graduate study of the subject. Exercises to sharpen the intuition and indicate further results are included at the end of each chapter.
In the first chapter, a number of examples of survival data are presented, each exhibiting a particular type of dependence. In some sets, the survival times are related within a group but independent between groups giving rise naturally to random effects or fraility models; in others dependence arises through multiple events and lead to multi-state models. Some of the sets of data exhibit both features. These and other sets of data are used to motivate models, either ones of increasing complexity and/or others that highlight different aspects of the data.
Each model is discussed in detail, interpreted, evaluated and compared with others. Both parametric and non-parametric models are considered and the purpose of each model is made clear. The author has a remarkable gift of illustrating abstract concepts with concrete examples. Detailed cross-referencing make the text easy to read. Many of the models cannot be fitted with commercially available software but sufficient detail and comment on the numerical behaviour is given to enable a competent programmer to implement them.
This book, however, is much more than a compendium of useful models for survival data. The author's discussion of time scales, the effect of censoring and the role of covariates touch the very heart of survival analysis. His insights into the nature of dependence extend far beyond survival analysis and touch on some of the most fundamental aspects of our discipline.
The book by Therneau and Grambsch, [Short Book Reviews, Vol.21, p. 5] has shown what can be done today with widely available statistical software. Hougaard's book shows why we do it and points to what we shall be able to do tomorrow. Together these books will have a wide impact on the use of a statistical technique whose importance is beginning to be appreciated far beyond the medical and industrial fields that originally motivated it.

Contents:
PART A: Meta-Analysis Methodology: The Basics
1. Introduction meta-analysis: Its development and uses
2. Defining outcome measures used for combining via meta-analysis
3. Assessing between study heterogeneity
4. Fixed effects methods for combining study estimates
5. Random effects models for combining study estimates
6. Exploring between study heterogeneity
7. Publication Bias
8. Study quality
9. Sensitivity analysis
10. Reporting the results of a meta-analysis
PART B: Advanced and Specialized Meta-Analysis Topcs
11. Bayesian methods in meta-analysis
12. Meta-analysis of individual patient data
13. Missing data
14. Meta-analysis of different types of data
15. Meta-analysis of multiple and correlated outcome measures
16. Meta-analysis of epidemiological and other observational studies
17. Generalized synthesis of evidence-combining different sources of evidence
18. Meta-analysis of survival data
19. Cumulative meta-analysis
20. Miscellaneous and developing areas of application in meta-analysis
APPENDIX I: Software Used for Examples in this Book

This book represents an expansion of the authors' review paper on methodology for meta-analysis published in 1998. The review material has been revised, updated and worked examples have been added. In addition, a description of how to carry out each illustrative example is included in an Appendix and a companion website for the book has been developed.
The very readable book will be very useful as an introduction to methods for meta-analysis and as a reference volume. The discussion in the book is well balanced and a thorough initial reading of the book, before using it as a reference for individual topics, would be a good investment of time. The brief discussion/summary comments on NNT (number needed to treat), the comparison of random and fixed effect models, and the use of individual patient data provide good examples of the authors' insight. However, for a few topics, some readers may feel the book stops short and gives less attention than appropriate to more general issues and methods. For example, likelihood based methods and general regression models receive relatively brief treatment and a reference is given for Zelen's exact test for homogeneity of an odds ratio without pointing out that the asymptotic version given in the same paper is known to be flawed. References for further reading are given frequently however.
Some concern about the current status of meta-analysis in medical research may be justified. However, it is widely used and this excellent book should improve the quality of its application.

Contents:
1. Molecular biology
2. Math primer
3. Sequence alignment
4. All about Eve
5. Hidden Markov models
6. Structure prediction
APPENDIX A: Mathematical Background
APPENDIX B: Resources

Readership: Advanced undergraduate and postgraduate students in bioinformatics, computer science, statistics, mathematics and biological sciences, and researchers in these fields

Computational biology, also known as bioinformatics, involves the practical and theoretical study of the structure of biological molecules. The analysis of the vast amounts of data being generated via gel electrophoresis needs trained researchers using sophisticated computer algorithms. This book aims to povide the requisite interdisciplinary tools and understanding.
The first two chapters give concise overviews of relevant biochemistry, structure of nuclei, probability theory, combinatorial mathematics, and information theory.
Subsequent chapters focus on dynamic programming sequence alignment algorithms, algorithms for the construction of phylogenetic trees (clustering methods, maximum likelihood, and quartst puzzling), the formulation of statistical models using hidden Markov models, and protein structure prediction (the protein folding problem). Readers will need perseverance and would appreciate guidance if they are to master all this.
End-of-chapter exercises are provided and useful resources, including errata, can be obtained by following links from the Wiley web page (http://www.wiley.co.uk/statistics ).
Such is the rapidity with which computational biology is developing (compare with Michael Waterman's "Introduction to Computational Biology: Maps, Sequences and Genomes". 1995 Chapman and Hall), the book cannot remain up-to-date for very long. Nevertheless, given frequent revision, its clarity and cohesion may well make it a classic text in this exciting new discipline.

Contents:
1. Introduction
2. The likelihood function
3. Division of sample information I: Likelihood č, model f
4. Division of sample information II: Likelihood structure
5. Estimation statements
6. Test of significance
7. The location-scale pivotal model
8. The Gauss linear model
9. Maximum likelihood estimation
10. Controlled experiments

Readership: Students and practitioners of statistics with some prevous exposure to probability and statistics

The book's basic premise is that (i) science is concerned with repeatable experiments; (ii) the data y can be modeled as coming from a hypothetical infinite population of possible observations having probabilities f(yi,č); (iii) once y has been observed, probability statements are no longer relevant and all that matters is the likelihood function f(y,č) as a function of č.
The principal tools for inference concerning č are the graph of the likelihood function and sets of "plausible" values of č, i.e. values for which the likelihood exceeds a given constant. Connections between such likelihood intervals and confidence, fiducial and Bayes intervals are established through the consideration of pivotal quantities. In addition to inferences about č, the problem of testing the model is considered. The tests are carried out in terms of traditional p-values.
On this basis the author builds an unconventional but rich and cohesive approach with applications to many of the standard problems considered in more traditional texts. The material is presented as a first course, with a probability but no statistics prerequisite. However, I believe that it is more suitable for students with previous exposure to a more traditional treatment. For such a reader it can be highly recommended as an enjoyable and stimulating introduction to an alternative point of view.

Contents
1. Introduction and preliminaries
2. Some principles of hypothesis testing
3. Parameter estimation and asymptotics
4. Inferences for classes of processes
5. Likelihood ratios for processes
6. Sampling methods for processes
7. More on stochastic inference
8. Prediction and filtering of processes
9. Nonparametric estimation for processes

This is an impressive book dealing with the classical statistical inference for stochastic processes. General versions of the maximum likelihood principle of Fisher and the fundamental lemma of Neyman and Pearson are the basis for parameter estimation and hypothesis testing. The classes of stochastic processes considered are: Gaussian, infinitely divisible, jump Markov, diffusion and adaptive. The work is of a high mathematical quality and is written in a format with theorems and proofs. Each chapter ends with bibliographical notes, complements and exercises. The latter make the book also interesting for teaching graduate courses.

Contents:
1. Introduction
2. Experiments, deficiencies, distances
3. Contiguity – Hellinger transforms
4. Gaussian shift and Poisson experiments
5. Limit laws and likelihood ratios
6. Local asymptotic normality
7. Independent, identically distibuted observations
8. On Bayes procedures

Lucien Le Cam, one of the founding fathers of modern asymptotic theory for statistical inference, completed this second edition of the 1990 book just before his death on April 25, 2000. It is co-authored with Grace Lo Yang, and as they say in the introduction, it is 'revised and enlarged'. The main change is the inclusion of a new Chapter 4 of about twenty-five pages on 'Gaussian Shift and Poisson Experiments'. They are very important in modelling and also as limits of other experiments. Several other chapters have been augmented with new material, and various proofs have been reworked. Some important topics have not been taken up in this monograph, but references to recent books have been given. It is a very valuable book giving a coherent view of the basic concept and tools of the asymptotic theory in statistical inference.

Contents:
1. Elements of stochastic processes
2. Local asymptotic normality for stochastic processes
3. Asymptotic theory of estimation and testing for stochastic processes
4. Higher order asymptotic theory for stochastic processes
5. Asymptotic theory for long-memory processes
6. Statistical analysis based on functionals of spectra
7. Discriminant analysis for stationary time series
8. Large deviation theory and saddlepoint approximation for stochastic processes

This book is a thorough survey of statistical inference methods for various classes of stochastic processes. The inference methods are based on asymptotics and include testing, estimation, discriminant and cluster analysis, nonparametric methods, large deviation results, saddle-point approximations, etc. Le Cam's concept of local asymptotic normality plays a fundamental role in the approach. There is a rich bibliography with more than four hundred items. The problem sections at the end of each chapter make the book also suitable for advanced course-work in stochastic processes.

Contents:
1. Point processes
2. Markov point processes
3. Statistical inference
4. Applications

In an increasing number of important areas of application, the basic data are spatial in nature. In this monograph, a brief overview of one class of probability models for such data is given that permits interactions between points, as long as the inter-point dependencies are determined by neighbours. The requisite background in general point processes is included. Some applications are used throughout for motivation, with more than half of the book devoted to topics of statistical inference (including Monte Carlo and maximum likelihood methods) and subsequent detailed and instructive applications. This book will be a useful reference in an area of considerable current activity.

Contents:
1. Random variables
2. Markov chains and random walks
3. Random elements
4. Stochastic processes
5. Shift-coupling
6. Markov processes
7. Transformation coupling
8. Stationarity, the Palm dualities
9. The Palm dualities in higher dimensions
10. Regeneration

Readership: Probabilists, theoretical statisticians working in Markov chain Monte Carlo

Coupling has been a tool in the probabilist's workbox for many years now. While tremendously useful for the expert, its use can meet resistance. Mathematicians are prone to claim "that's cheating" when confronted by a construction of two random processes carefully chosen to be independent in such a way as to make a proof easy.
This book begins with an overview of some important examples of coupling (Chapters 1 and 2), then proceeds to a careful exposition of measure-theoretic details (Chapters 3 to 6) which is ideal for the purpose of silencing idle mathematical hecklers. Already in these chapters the author brings in some of his own gifts to coupling theory (equivalences between various kinds of coupling, asymptotics, and ó-algebra properties).
The book is completed by three long chapters (Chapters 8, 9 and 10) providing sustained accounts of the author's particular contributions; invaluable and stimulating reading. The book is not, nor is it intended to be, an encyclopaedia of the wide diversity of coupling methods, nor is it intended to give an authoritative historical overview (there are useful remarks in the notes, but the author confesses to having sacrificed historical completeness to the end of actually getting the book published in finite time). What the book does offer is a careful, stimulating, and original discussion of major themes in coupling. As such, it will be invaluable to probabilists and also to the increasing number of statisticians working on Markov Chain Monte Carlo and especially perfect simulation.

Contents:
1. Introduction
2. Some general tools and results
3. The compound Poisson model
4. The probability of ruin within finite time
5. Renewal arrivals
6. Risk theory in a Markovian environment
7. Premiums depending on the current reserve
8. Matrix-analytic methods
9. Ruin probabilities in the presence of heavy tails
10. Simulation methodology
11. Miscellaneous topics

This book is a must for anybody working in applied probability. It is a comprehensive treatment of the known results on ruin probabilities, in particular covering the author's research in the area. Its extensive bibliography (including queueing literature) also makes it useful for finding references. Especially nice are the sample path arguments used in many of the proofs. Examples illustrate the theory. Moreover, related topics like sensitivity estimates or rare-events simulation are discussed.

Contents:
Introduction
1. The Black-Scholes theory of derivative pricing
2. Introduction to stochastic volatility models
3. Scales in mean-reverting stochastic volatility
4. Tools for estimating the rate of mean reversion
5. Asymptotics for pricing European derivatives
6. Implementation and stability
7. Hedging strategies
8. Application to exotic derivatives
9. Application to American derivatives
10. Generalizations
11. Applications to interest-rate models

From the start, financial engineers knew that the conditions on constant volatility in the basic Black-Scholes-Merton (BSM) approach to option pricing and hedging was only an approximative one. Early on, smile effects pointed at a need to model beyond this constant volatility. As a consequence, the world of GARCH modelling together with stochastic volatility models emerged. The present book discusses the latter. Its first half contains a very readable introduction to the probabilistic theory of stochastic volatility modelling. Gradually, the authors pencil in the statistical proofs of volatility bursts and fast mean reversion. Based on these empirical facts, an asymptotic expansion approach is used to correct the pricing and hedging formulae in the classical BSM world. Along the way, two new "Greeks", epsilon and kappa, are introduced. They correspond to the third and fourth derivative of the classical Black-Scholes price with respect to the price of the underlying. The corrected formulae are tested on some real examples including more exotic options. The book is well written and makes ideal reading for a graduate course on mathematical finance. The authors took great care in making their ideas clear. I support this text strongly and recommend it for the intended audience.

Contents:
1. Introduction
2. Some concepts in time series analysis
3. Regime-switching models for returns
4. Regime-switching models for volatility
5. Artificial neural networks for returns
6. Conclusions

Readership: Advanced undergraduate or graduate students having a background in mathematics and econometrics, academics and time-series practitioners seeking an introduction to nonlinear modelling

This textbook provides an up-to-date guide to recently developed models incorporating non-linearity, in particular regime-switching models and artificial neural networks. Nonlinear models allow for the atypical events and asymmetry seen in financial series. A wide range of financial data series are used to illustrate the application of these methods to describe returns on assets and associated volatilities. The models incorporate autoregressive modelling: switching between AR models, with GARCH and its extensions for volatility analysis.
Reasons for choosing the models described are given, and this will encourage judicious choices from the massive number of potential nonlinear models. This should reduce dependence on the systematic testing of recipes for a good fit. I can think of no better introduction to nonlinear statistical modelling

Contents:
1. Random walks and first step analysis
2. First martingale steps
3. Brownian motion
4. Martingales: The next steps
5. Richness of paths
6. Itô integration
7. Localization and Itô's integral
8. Itô's formula
9. Stochastic differential equations
10. Arbitrage and SDEs
11. The diffusion equation
12. Representation theorems
13. Girsanov theory
14. Arbitrage and martingales
15. The Feynman-Kac connection
APPENDIX I: Mathematical Tools
APPENDIX II: Comments and Credits

Readership: Anyone with an interest in probability and finance, university level mathematics and probability theory

This is a world of "lovely exercises" that are "very good for the soul", "honest martingales", "bedrock approximations", portfolios that are "born to lose", "intuitive but bogus arguments", and "embarrassingly crude insights". In short, this is a book on stochastic calculus of a different flavour. Intuition is not sacrificed for rigour nor rigour for intuition. The main results are reinforced with simple special cases, and only when the intuitive foundations are laid does the author resort to the formalism of probability. The coverage is limited to the essentials but nevertheless includes topics that will catch the eye of experts (such as the wavelet construction of Brownian motion). This is one of the most interesting and easiest reads in the discipline; a gem of a book.

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

Reviewer:
Institute	University of Waterloo
Place	Waterloo, Canada
Name	R.W. Oldford

Reviewer:
Institute	Imperial College of Science, Technology and Medicine
Place	London, U.K.
Name	F.H. Berkshire

Reviewer:
Institute	National Research Council of Canada
Place	Ottawa, Canada
Name	D.A. Ramsay

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

Title	OPTIMIZATION: FOUNDATIONS AND APPLICATIONS.
Author	R.E. Miller.
Publisher	New York: Wiley, 2000, pp. xvii + 653, Ł58.50.

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

Reviewer:
Institute	Isfahan University of Technology
Place	Isfahan, Iran
Name	A. Parsian

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

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

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

Reviewer:
Institute	University of Manchester Science and Technology
Place	Manchester, U.K.
Name	T. Subba Rao

Reviewer:
Institute	Technology and Medicine
Place	London, U.K.
Name	M. Crowder

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

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

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

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

Reviewer:
Institute	University of Toronto
Place	Toronto, Canada
Name	D.F. Andrews

Reviewer:
Institute	Univerity of Waterloo
Place	Waterloo, Canada
Name	D.L. McLeish

Reviewer:
Institute	CSIRO
Place	Melbourne, Australia
Name	R.G. Jarrett

Reviewer:
Institute	University of Maryland
Place	College Park, U.S.A.
Name	J.D. Picka

Reviewer:
Institute	University of Manchester Institute of Science and Technology
Place	Manchester, U.K.
Name	T. Subba Rao

Reviewer:
Institute	Zürcher Kantonalbank
Place	Zürich, Switzerland
Name	P. Vanini

Reviewer:
Institute	University of Wiscosin
Place	Madison, U.S.A.
Name	K.-W. Tsui

Reviewer:
Institute	Isfahan Univerisity of Technology
Place	Isfahan, Iran
Name	A. Parsian

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

Reviewer:
Institute	London School of Hygiene and Tropical Medicine
Place	London, U.K.
Name	B.L. De Stavola

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

Reviewer:
Institute	University of Texas
Place	Austin, U.S.A.
Name	P.W.M. John

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

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

Reviewer:
Institute	University of Kent
Place	Canterbury, U.K.
Name	B.J.T. Morgan

Reviewer:
Institute	University of Cambridge
Place	Cambridge, U.K.
Name	P. Whittle

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

Reviewer:
Institute	AT&T Redbank, U.S.A. and Royal Holloway College
Place	London, U.K.
Name	V.N. Vapnik