Plans d’expérience: constructions et analyses statistiques by Walter Tinsson

International Statistical Review (2011), 79, 1, 114–143 doi:10.1111/j.1751-5823.2011.00134.x

Short Book ReviewsEditor: Simo Puntanen

Graphics for Statistics and Data Analysis with RKevin J. KeenChapman & Hall/CRC, 2010, xxxiv + 447 pages, £39.99/$69.95, hardcoverISBN: 978-1-58488-087-5

Table of contents

1. The graphical display of information2. Basic charts for the distribution of a single

discrete variable3. Advanced charts for the distribution of a single

discrete variable4. Exploratory plots for the distribution of a

single continuous variable5. Diagnostic plots for the distribution of a

continuous variable6. Nonparametric density estimation for a single

continuous variable

7. Parametric density estimation for a singlecontinuous variable

8. Depicting the distribution of two discretevariables

9. Depicting the distribution of one continuousvariable and one discrete variable

10. Depicting the distribution of two continuousvariables

11. Graphical displays for simple linear regression12. Graphical displays for polynomial regression13. Visualizing multivariate data

Readership: Students wanting to learn about graphical design for statistical graphics.

“This book is intended for those wanting to learn about the basic principles of graphical designas applied to the presentation of data.” So it is about the how and not the why of graphics. Itis mainly restricted to one and two dimensional graphics with just a short, and consequentlydisappointing chapter on visualizing multivariate data at the end. A lot of the recommendationsare sound, though providing twenty-one alternative versions of the fourteen data points makingup the United Nations budget for 2008–9 was a strange decision, especially as the plots aremostly on different pages, so that comparisons are difficult. It is also surprising that three ofthese versions are coloured pie charts (including one pseudo three-dimensional exploded piechart). Given that there are only eight pages of colour displays in the whole book, you wouldthink that the author would take the opportunity to present something more attractive. And thereis the rub. An unscientific, if nevertheless revealing, test of any graphics book is whether thereare graphics in it that you would show to someone else and say “Look at that, isn’t it great?”There is not one such graphic here. What you get in the book is some sensible advice, somesnippets of R code, a number of bad graphics (which the author rightly criticises), and a numberof slightly better graphics.

Antony Unwin: [email protected] Augsburg, Institut fur Mathematik

D-86135 Augsburg, Germany

C© 2011 The Author. International Statistical Review C© 2011 International Statistical Institute.. Published by Blackwell Publishing Ltd, 9600 GarsingtonRoad, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

SHORT BOOK REVIEWS 115

Data Analysis and Graphics Using R: An Example-based Approach, Third EditionJohn Maindonald, W. John BraunCambridge University Press, 2010, xxvi + 525 pages, £50.00/$80.00, hardcoverISBN: 978-0-521-76293-9

Table of contents

1. A brief introduction to R2. Styles of data analysis3. Statistical models4. A review of inference concepts5. Regression with a single predictor6. Multiple linear regression7. Exploiting the linear model framework8. Generalized linear models and survival analysis9. Time series models

10. Multi-level models and repeated measures11. Tree-based classification and regression12. Multivariate data exploration and

discrimination13. Regression on principal component or

discriminant scores14. The R system—additional topics15. Graphics in R

Readership: Scientists wishing to do statistical analysis on their own data.

This is a slightly expanded edition of a well-known text. Interestingly, the authors say that theyhave rewritten the treatment of one-way anova and a major part of the chapter on regression. Nowwhy would they have decided to do that? They have also included more on errors in predictorvariables and on random forests. Finally, there is an additional chapter on graphics in R. Thebook’s strengths are its sound practical advice, its readability (mathematical symbolism is playeddown), the many real datasets, and the extensive use of R. The datasets are from a variety ofapplications and are generally worth studying. They are all rather small, which is not so realisticthese days, though it is appropriate for the book’s intended readership. There is an accompanyingR package for the book, which contains most of the datasets. As is typical for R help files, thecode for the examples provided in the package is only for illustration and not for analysis. Ifyou want to see how the authors suggest the data are analysed, you need the book. The book’smain weakness is its graphics. They are generally disappointing and not as informative as theycould or should be. In other words, they are as good as the graphics you find in most statisticstextbooks.



International Statistical Review (2011), 79, 1, 114–143C© 2011 The Author. International Statistical Review C© 2011 International Statistical Institute.

116 SHORT BOOK REVIEWS

Mathematics and SportsJoseph A. Gallian (Editor)Mathematical Association of America, 2010, xi + 329 pages, $39.95, softcoverISBN: 978-0-88385-349-8

Table of contents

I Baseball1. Sabermetrics: the past, the present, and the

future (Jim Albert)2. Surprising streaks and playoff parity:

probability problems in a sports context (RickCleary)

3. Did humidifying the baseball decrease thenumber of homers at Coors field? (HowardPenn)

4. Streaking: finding the probability for a battingstreak (Stanley Rothman, Quoc Le)

II Basketball5. Bracketology: how can math help? (Tim

Chartier, Erich Kreutzer, Amy Langville,Kathryn Pedings)

6. Down 4 with a minute to go (G. Edgar Parker)7. Jump shot mathematics (Howard Penn)

III Football8. How deep is your playbook? (Tricia Muldoon

Brown, Eric B. Kahn)9. A look at overtime in the NFL (Chris Jones)

10. Extending the Colley method to generatepredictive football rankings (R. Drew Pasteur)

11. When perfect isn’t good enough: retrodictiverankings in college football (R. Drew Pasteur)

IV Golf12. The science of a drive (Douglas N. Arnold)

13. Is Tiger Woods a winner? (Scott M. Berry)14. G. H. Hardy’s golfing adventure (Roland

Minton)15. Tigermetrics (Roland Minton)V NASCAR16. Can mathematics make a difference? Exploring

tire troubles in NASCAR (Cheryll E. Crowe)VI Scheduling17. Scheduling a tournament (Dalibor Froncek)VII Soccer18. Bending a soccer ball with math (Tim Chartier)VIII Tennis19. Teaching mathematics and statistics using

tennis (Reza Noubary)20. Percentage play in tennis (G. Edgar Parker)IX Track and Field21. The effects of wind and altitude in the 400m

sprint with various IAAF track geometries(Vanessa Alday, Michael Frantz)

22. Mathematical ranking of the division III trackand field conferences (Chris Fisette)

23. What is the speed limit for men’s 100 meterdash? (Reza Noubary)

24. May the best team win: determining the winnerof a cross country race (Stephen Szydlik)

25. Biomechanics of running and walking(Anthony Tongen, Roshna E. Wunderlich)

Readership: Everyone with sporting interests listed in the chapters.

This is a book intended to demonstrate the illuminating power of mathematics to a largeraudience, and the chapters were solicited for the 2010 Mathematics Awareness Month. It is anexcellent, entertaining and informative work with something to satisfy every reader. Read thisbook on a bus, train or plane and you will find yourself saying “Are we here already?”

Norman R. Draper: [email protected] of Statistics, University of Wisconsin – Madison

1300 University Avenue, Madison, WI 53706-1532, USA



A Comparison of the Bayesian and Frequentist Approaches to EstimationFrancisco J. SamaniegoSpringer, 2010, xiii + 225 pages, €69.95/£62.99/$79.95, hardcoverISBN: 978-1-4419-5940-9

Table of contents

1. Point estimation from a decision-theoreticviewpoint

2. An overview of the frequentist approach toestimation

3. An overview of the Bayesian approach toestimation

4. The threshold problem5. Comparing bayesian and frequentist estimators

of a scalar parameter6. Conjugacy, self-consistency and Bayesian

consensus

7. Bayesian vs. frequentist shrinkage inmultivariate normal problems

8. Comparing Bayesian and frequentist estimatorsunder asymmetric loss

9. The treatment of nonidentifiable models10. Improving on standard Bayesian and

frequentist estimators11. Combining data from “related” experiments12. Fatherly adviceAppendix: Standard univariate probability models

Readership: Intended to be broad, including an advanced undergraduate audience, but studentsmay lack the necessary maturity for this endeavour and the book would more likely benefit moresenior readers.

A Comparison is pleasant to read, written in a congenial style (especially the final “fatherlyadvices”!), and the decision-theoretic background is well-set. Its self-declared purpose of“identify[ing] the boundary between Bayes estimators which tend to outperform standardfrequentist estimators and Bayes estimators which don’t” is commendable in that an objectivecomparison of Bayesian versus frequentist estimators should appeal to anyone. However, thefocus of A Comparison ends up being too narrow to appeal to a wide audience, given that thebook revolves around papers written jointly or singly by the author on this topic and that it is setwithin a point estimation framework where there exists a “best” unbiased estimator, a conditionabsent from most estimation problems (Lehmann & Casella, 1998). (Other inferential aspectslike testing are not covered.)

Towards the comparison of frequentist and Bayesian procedures, since under a given priorG, the optimal procedure always is associated with G, A Comparison introduces a “true prior”G0 that should calibrate the comparison. Unsurprisingly, the conclusion is that if G is closeenough to G0, then the Bayesian procedure does better than the frequentist one. Since thisimprovement depends on an unknown “truth”, the practical implications are limited. From aBayesian perspective, inference under “wrong” priors has been studied in the 90’s as Bayesianrobustness (Insua & Ruggeri, 2000).

A Comparison insistance in using conjugate (proper) priors is inappropriate in conjunctionwith shrinkage estimation, since truly Bayesian shrinkage estimators correspond to hierarchicalpriors (Berger & Robert, 1990). Furthermore, the appeal of self-consistency (Chapter 6) islimited: a prior is self-consistent if, when prior expectation and observation coincide, priorand posterior expectations are equal. This constraint focuses on a zero probability event and isnot parameterisation-invariant, while being restricted to natural conjugate priors, for example,excluding mixtures of conjugate priors.

Chapter 9 offers a new perspective on non-identifiability, but focuses on the performancesof the Bayesian estimates of the non-identifiable part. The appeal of the Bayesian approach israther to infer on the identifiable part by integrating out non-identifiable parameters. Chapters



10–11 about combining experiments are interesting but a modern Bayesian analysis would resortto a non-parametric modelling rather than to empirical Bayes techniques.

In conclusion, A Comparison does not revolutionise the time-old debate about the relevanceof Bayesian procedures towards frequentist efficiency or about relying on frequentist estimatesunder weak prior information. Given my reservations, I would have difficulties to advertise it asa textbook

Christian P. Robert: [email protected]—Universite Paris-Dauphine, Bureau B638

Place du Marechal de Lattre de Tassigny, 75775 PARIS Cedex 16, FRANCE

References

Berger, J.O. & Robert, C. (1990). Subjective hierarchical Bayes estimation of a multivariate normal mean: on thefrequentist interface. Ann. Statist., 18, 617–651.

Insua, D.R. & Ruggeri, F. (Eds.) (2000). Robust Bayesian Analysis. New York: Springer.Lehmann, E.L. & Casella, G. (1998). Theory of Point Estimation, 2nd ed. New York: Springer.

Design and Analysis of Experiments with SASJohn LawsonChapman & Hall/CRC, 2010, xiii + 582 pages, £63.99/$99.95, hardcoverISBN: 978-1-4200-6060-7

Table of contents

1. Introduction2. Completely randomized designs with one factor3. Factorial designs4. Randomized block designs5. Designs to study variances6. Fractional factorial designs7. Incomplete and confounded block designs

8. Split-plot designs9. Crossover and repeated measure designs

10. Response surface designs11. Mixture experiments12. Robust parameter design experiments13. Experimental strategies for increasing

knowledge

Readership: Experimenters and their statistical colleagues.

This is specifically a book on response surface methodology written for those who use theSAS computing system. Consequently, its appeal is somewhat limited, because all explanationsof experimental designs and their uses quickly merge into the consequent SAS programmingmethods required to get such designs and perform the appropriate analyses. The expositionthroughout is first rate. The presentation and organization, the coverage of the topics, andthe discussions of the examples are all excellent. If you are an SAS user needing help withexperimental design, you will certainly profit from this text.





Principles and Theory for Data Mining and Machine LearningBertrand Clarke, Ernest Fokoue, Hao Helen ZhangSpringer, 2009, xv + 781 pages, €64.95/£58.99/$79.95, hardcoverISBN: 978-0-387-98134-5

Table of contents

1. Variability, information, and prediction2. Local smoothers3. Spline smoothing4. New wave nonparametrics5. Supervised learning: partition methods6. Alternative nonparametrics

7. Computational comparisons8. Unsupervised learning: clustering9. Learning in high dimensions

10. Variable selection11. Multiple testing

Readership: PhD level students, and researchers and practitioners in statistical learning andmachine learning.

Data Mining may be seen as a response to the new demands that have been generated by largehigh-dimensional (many variables) data sets, by new methodologies that take advantage of thepower of modern computing systems, and by the emergence of new data analysis techniquesthat are a marked departure from more classical approaches. Machine Learning emphasizes theuse of formal structures that allow machines (computers) to automate important componentsof inferential procedures. With “high-dimensional” data, model uncertainty often becomes adominant issue for the analyst. The first chapter has insightful and interesting comment on thecurse of dimensionality, sparsity, exploding numbers of models, multicollinearity and concurvity,the effect of noise, local dimension, and parsimony. There is a note on the selection of designpoints for computer experiments.

This text assumes a thorough training in undergraduate statistics and mathematics. Computedexamples that include R code are scattered through the text. There are numerous exercises, manywith commentary that sets out guidelines for exploration.

As with most texts in this area, the independent, symmetric unimodal error model is assumedthroughout. In comparing nonparametric regression with linear regression the authors commentthat people tend to put less emphasis on the error structure than on uncertainty in estimates ofthe functional form f . They argue that:

“This is reasonable because, outside of large departures from independent, symmetric, unimodal εis,the dominant sources of uncertainty come from estimating f .”

This grossly downplays the importance of temporal and spatial error structures, and of layeredstructures of variation, in many of the large high dimensional data sets that analysts nowadaysencounter. The over-riding reason for staying with the independent, symmetric unimodal errormodel is surely that no one book can cover everything! Within these bounds, this book gives acareful treatment that is encyclopedic in its scope.

The book divides into three parts. Part I (chapters 1–4) is on nonparametric regression; PartII (chapters 5–7) is a mix of classification and recent nonparametric methods that includescomputational comparisons; Part III (chapters 8–11) covers high-dimensional problems thatinclude clustering, dimension reduction, variable selection and multiple comparisons.



This is a challenging text that is thorough in its coverage of technical issues.

John H. Maindonald: [email protected] for Mathematics & Its Applications

Australian National University, Canberra ACT 0200, Australia

Bayesian Model Selection and Statistical ModelingTomohiro AndoChapman & Hall/CRC, 2010, xiv + 286 pages, £63.99/$89.95, hardcoverISBN: 978-1-4398-3614-9

Table of contents

1. Introduction2. Introduction to Bayesian analysis3. Asymptotic approach for Bayesian inference4. Computational approach for Bayesian inference5. Bayesian approach for model selection

6. Simulation approach for computing themarginal likelihood

7. Various Bayesian model selection criteria8. Theoretical development and comparisons9. Bayesian model averaging

Readership: Statistics graduate students and researchers in Bayesian model choice.

While Bayesian model selection is one of my favourite research topics, I am alas disappointedafter reading this book. First, the innovative part of the book is mostly based on papers writtenby the author over the past five years, revolving around the Bayesian predictive informationcriterion (BPIC, Ando, 2007). Second, the more general picture constitutes a regression whencompared with existing books like Chen et al. (2000). The coverage of the existing literature isoften incomplete and sometimes confusing. This is especially true for the computational aspectsthat are generally poorly treated or at least not treated in a way from which a newcomer to the fieldwould benefit. For instance, the Metropolis–Hastings algorithm (page 66) is first introduced ina Metropolis-within-Gibbs framework, however the acceptance probability forgets to accountfor the other components of the parameter; or Chapter 6 opts for the worst possible choice inthe “Gelfand–Day’s” (sic!) and bridge sampling estimators by considering the harmonic meanversion with the sole warning that it “can be unstable in some applications” (page 172).

The author often uses complex econometric models as illustrations, which is nice; however,he does not pursue the details far enough for a reader to replicate the study without furtherreading. The few exercises in each chapter are rarely helpful, more like appendices. Take, forexample, Exercise 6, page 196, which (re-)introduces the Metropolis–Hastings algorithm, eventhough it has already been defined on page 66, and then asks the reader to derive a marginallikelihood estimator. Another exercise on page 164 covers the theory of DNA micro-arrays andgene expression in ten lines (repeated verbatim page 227), then asks the reader to identify markergenes responsible for a certain trait.

The quality of the editing is quite poor, with numerous typos throughout the book. For instance,as a short sample of those, Gibbs sampling is spelled Gibb’s sampling (only) in Chapter 6, thebibliography is not printed in alphabetical order and contains erroneous entries, like Jacquier,Nicolas and Rossi (2004) or Tierney and Kanade (1986), some sentences are not grammaticallycorrect (for example, “the posterior has multimodal”, page 55) or meaningful (for example, “theaccuracy of this approximation on the tails may not be accurate”, page 49).

After reading this book, I feel the contribution to the field of Bayesian Model Selection andStatistical Modeling is too limited and disorganised for the book to be recommended as “helping



you choose the right Bayesian model” (as advertised on the back-cover). It certainly falls shortof being an appropriate textbook for most audiences.

Christian P. Robert: [email protected]—Universite Paris-Dauphine, Bureau B638

Place du Marechal de Lattre de Tassigny, 75775 PARIS Cedex 16, FRANCE

References

Ando, T. (2007). Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empiricalBayes models. Biometrika, 94, 443–458.

Chen, M., Shao, Q. & Ibrahim, J. (2000). Monte Carlo Methods in Bayesian Computation. New York: Springer.

Statistical Inference: An Integrated Bayesian/Likelihood ApproachMurray AitkinChapman & Hall/CRC, 2010, xvii + 236 pages, £57.99/$89.95, hardcoverISBN: 978-1-4200-9343-8

Table of contents

1. Theories of statistical inference2. The integrated Bayes/likelihood approach3. t-Tests and normal variance tests4. Unified analysis of finite populations

5. Regression and analysis of variance6. Binomial and multinomial data7. Goodness of fit and model diagnostics8. Complex models

Readership: Graduate or advanced undergraduate statisticians of all philosophies, especiallyBayesians.

This book describes an approach to inference based on using the likelihood function as theprimary measure of evidence for parameters and models. The emphasis on evidence rather thandecision theory makes the book especially relevant to scientific investigations.

It gives interesting and thoughtful comparisons to alternative approaches to inference, arguingthat that presented here has particular strengths. In place of Bayes factors to compare models, astrategy using the full posterior distribution of the likelihood is described. It also shows that theapproach provides a natural strategy for finite population inference.

The author describes the overall result as providing a “general integrated Bayesian/likelihoodanalysis of statistical models”, to serve as an alternative to standard Bayesian inference andas a foundation “for a course sequence” in modern Bayesian theory. The very deep and solidinferential foundations the book lays support a matching carefully thought out and impressivesuperstructure, covering topics which include variance component models, finite mixtures,regression, anova, complex survey designs, and other topics.

It would provide a valuable and thought provoking volume for advanced students studyingthe foundations of inference and their practical implications. It would make a particularly goodbook for a reading group.

David J. Hand: [email protected] Department, Imperial College

London SW7 2AZ, UK



Charming Proofs: A Journey into Elegant MathematicsClaudi Alsina, Roger B. NelsenMathematical Association of America, 2010, xxiv + 295 pages, $59.95, hardcoverISBN: 978-0-88385-348-1

Table of contents

Introduction1. A garden of integers2. Distinguished numbers3. Points in the plane4. The polygonal playground5. A treasury of triangle theorems6. The enchantment of the equilateral triangle

7. The quadrilaterals’ corner8. Squares everywhere9. Curves ahead

10. Adventures in tiling and coloring11. Geometry in three dimensions12. Additional theorems, problems and proofsSolutions to the challenges

Readership: Secondary school, college, and university teachers, or indeed anyone who enjoysthe aesthetics of mathematics.

This is a collection of remarkable proofs, all using elementary mathematical or geometricalarguments, and all very simple but often extraordinarily powerful. While some will be wellknown, I imagine that almost every reader will find material here that they have not encounteredbefore.

Although the book is a mathematics book, I feel sure that some of the theorems would havedirect relevance to statistics. For example, how about: for any even number of different pointsdistributed inside a circle it is always possible to draw a line across the circle missing everypoint and such that exactly half lie on each side of the line. Surely this can find application insegmentation analysis, for applications in marketing and other areas.

In addition to the proofs themselves, there are over 130 “challenges” aimed at stimulating thereader to create similar such “charming proofs”. Solutions to these challenges appear at the endof the book.

I cannot help but feel that working carefully through the proofs in this book would materiallyimprove one’s creative powers and ability to think laterally.


London SW7 2AZ, UK



Maximum Penalized Likelihood Estimation, Volume II: RegressionPaul P. Eggermont, Vincent N. LaRicciaSpringer, 2009, xx + 571 pages, €74.95/£67.99/$99.00, hardcoverISBN: 978-0-387-40267-3

Table of contents

12. Nonparametric regression13. Smoothing splines14. Kernel estimators15. Sieves16. Local polynomial estimators17. Other nonparametric regression problems18. Smoothing parameter selection19. Computing nonparametric estimators

20. Kalman filtering for spline smoothing21. Equivalent kernels for smoothing splines22. Strong approximation and confidence bands23. Nonparametric regression in action

Appendix 4. Bernstein’s inequalityAppendix 5. The TVDUAL implementationAppendix 6. Solutions to some critical exercises

Readership: This book is meant for specialized readers or graduate students interested in thetheory, computation and application of Nonparametric Regression to real data, and the newcontributions of the authors.

A strong mathematical background from the reader is needed, even though the authors tryto make the presentation intuitively plausible before embarking on rigorous arguments. Formathematically mature readers, the book would be a delight to read. Many others, with agood background in cubic splines, may want to read this book to see the generalizations viaReproducing Kernel Hilbert Space (RKHS) and Kalman’s State Space models. Two real life datasets are analyzed both by the old and new methods.

This is the second volume of what is likely to be a trilogy, the third volume discussing inverseproblems. The first volume is a relatively sophisticated introduction to classical parametric andnonparametric methods. The second volume, that is, the volume under review, begins with anintroductory chapter on Nonparametric Regression, splines, and RKHS. Splines are developedmore fully in the second chapter. The next six chapters provide fairly detailed coverage of sieves,local polynomial estimators, non-smooth Nonparametric Regression, and computation.

The remaining four chapters provide what is the core of the book and its major newcontribution. Two chapters show how Kalman’s state space models lead to a convenient methodfor computing higher splines when data cannot be modeled with cubic splines. The next chapterprovides confidence bands. The last chapter returns to the two data sets introduced right atthe beginning. Much of this new work is connected earlier work on (diffuse) Gaussian processpriors. As Bayesians know well, diffuse priors are improper, hence source of many technicaldifficulties, but they are too useful to be given up.

The authors have not only written a scholarly and very readable book but provide major newmethods and insights. Nonetheless, it cannot be easy to offer a graduate course based on it. Butif there is a workshop based on the book at SAMSI (the NSF funded Statistics and AppliedMathematics Institute), then it would help evaluate the methods as well as lead to teachablenotes for a graduate course.

Jayanta K. Ghosh: [email protected] of Statistics, Purdue University

West Lafayette, IN 47909, USA



Probability, Statistics, & Financial MathPeter CaithamerPeter Caithamer, 2010, vii + 667 pages, $180.00, hardcoverISBN: 978-0-9830011-0-2

Table of contents

I Probability Theory1. Logic & set theory2. Probability measures3. Random variables and their distributions4. Stochastic processes

II Mathematical Statistics5. Estimation6. Hypothesis tests

7. Linear regressionIII Financial Mathematics

8. Interest theory9. Life contingencies

10. Options pricingSolutionsTables & charts

Readership: Undergraduate and graduate students in mathematical statistics, actuarial sciences,and finance. Actuary candidates preparing to actuarial exams. Actuaries and other professionalsin finance.

The textbook is written with the material for the core actuarial exams in mind and this stronglyinfluenced its scope which is truly staggering. Just to quote from the introduction: “It maybe used for 6 to 8 complete undergraduate/graduate courses on probability theory, stochasticprocess, mathematical statistics, regression & time series, credibility theory, interest theory,life contingencies, and option pricing.” One gets skeptical about the outcome if the goals areset so broadly in terms of the subject and the audience—it is obvious that something has to besacrificed along the way. Thus initially I was very doubtful about the final result, wondering if it ispossible at all to write a coherent exposition that would speak to an inexperienced undergraduatestudent on fundamentals of probability and statistics and at the same time address graduatelevel audience by explaining how Girsanov’s Theorem allows to reformulate no arbitrage rulein finance. Surprisingly, despite this daunting task the book delivers on the promises. It iswritten carefully and in notationally consistent manner. While discussing the topics from thewide spectrum of difficulty, it does it in a bold but honest manner not avoiding mathematicallyadvanced language when it cannot be avoided.

So where did it have to give away? By necessity it had to be very brief and by goingdirectly to the definitions and theorems it lacks on motivation and background. This isto great extend remedied by a well balanced set of exercises and problems with completesolutions provided in an appendix. However, the discussed topics are not placed in broaderperspective of the field to which they belong. For these reasons it is not a book that onewould pick up to read for enjoyment in free time. However, it will definitely be appreciatedwhen efficiency is needed during preparation for an examination in any of the covered fieldsof broadly understood probability theory and its applications. Since there is currently notextbook available with this scope, it is an important and quite successful first effort to fill thisgap.

It is evident that the book has been tested in the classroom and thus could be utilized asa textbook. However, when considered for this, it should be accompanied by some additionalenhancing texts or an additional effort should be made to give more motivation to a potential



audience. The book would also serve well as a study guide that can be used by students andprofessionals alike.

Krzysztof Podgorski: [email protected] for Mathematical Sciences

Lund Institute of Technology/Lund UniversityBox 118, 22100 Lund, Sweden

The Pleasures of Statistics: The Autobiography of Frederick MostellerFrederick Mosteller, Edited by Stephen E. Fienberg David C. Hoaglin, Judith M. TanurSpringer, 2010, xvi + 344 pages, €42.75/£35.99/$39.95, softcoverISBN: 978-0-387-77955-3

Table of contents

Part I. Examples of Quantitative StudiesIntroduction

1. Why did Dewey beat Truman in thepre-election polls of 1948?

2. Sexual behavior in the United States: TheKinsey report

3. Learning theory: Founding mathematicalpsychology

4. Who wrote the disputed Federalist papers,Hamilton or Madison?

5. The safety of anesthetics: The nationalhalothane study

6. Equality of educational opportunity: TheColeman report

Part II. Early Life and Education7. Childhood8. Secondary school

9. Carnegie Institute of Technology10. Graduate schools: Carnegie and Princeton11. Magic12. Beginning research13. Completing the doctorate14. Coming to Harvard University15. Organizing statistics

Part III. Continuing Activities16. Evaluation17. Teaching18. Group writing19. The Cape20. Biostatistics21. Health policy and management22. Health science policy23. Editors’ epilogue

Readership: All interested in statistical research, statistics in society, and academic life,particularly those for whom it is not too late to benefit from the wisdom in this book.

There are very few book-length autobiographies of statisticians, and so the appearance of onewill be of interest to most readers of this Review, as it was to me. However, I would be surprisedif many people other than those who knew Frederick Mosteller personally, or were alreadyvery familiar with his work, could anticipate the pleasure they will get from reading this book.Neither the title, the cover, a quick skim, or even a familiarity with the basics of Mosteller’scareer, would lead one to expect such a good book. It was pure joy to read it, though I must say Idid not begin at the beginning. Mosteller’s childhood during the Great Depression, his secondaryschool, college and graduate education, his activities during World War 2, and his early careersteps, were all much more interesting to me than the statistics case studies which occupy the firstthird of the book. It seemed to me to be a very American story (work hard, develop good habits,take opportunities when they present themselves, treat others well, etc.), and while it is not quite“rags to riches”, it has that feel about it. I could not help but think of Mark Twain. Full of wit,wisdom and sage advice, the book has much to offer those interested in the teaching of statistics,cross-disciplinary as well as narrow sense statistical research and academic administration, butperhaps most of all, it is written for those who believe in the power of statistics to help make the



world a better place. The entire book has a pedagogical rather than a tell-all style, which doesn’tseem out of place. On the contrary, it gives Mosteller the opportunity to explain a variety ofaspects of statistics to the lay reader, to put them in a larger context, and to comment on someof the people involved, at the same time revealing something about himself. This combinationof textbook and personal memoir is very appealing.

Terry Speed: [email protected] of Statistics, 367 Evans Hall #3860

University of California, Berkeley, CA 94720-3860, USA

Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and PredictionBradley EfronCambridge University Press, 2010, xii + 263 pages, £40.00/$65.00, hardcoverISBN: 978-0-521-19249-1

Table of contents

Introduction and foreword1. Empirical Bayes and the James–Stein estimator2. Large-scale hypothesis testing3. Significance testing algorithms4. False discovery rate control5. Local false discovery rates6. Theoretical, permutation, and empirical null

distributions

7. Estimation accuracy8. Correlation questions9. Sets of cases (enrichment)

10. Combination, relevance, and comparability11. Prediction and effect size estimationA. Exponential familiesB. Programs and data sets

Readership: Everyone interested in large-scale inference, and people interested in what’s newand different about 21st in comparison with 20th century statistics.

As we all will have noticed, a number of fields have emerged over the last few decades whichpresent inferential challenges not adequately met by the methods developed by Pearson, Fisher,Neyman, and their immediate successors. Mapping disease risk, brain imaging, and analysingmicroarray data are just three examples. Put very briefly, these challenges involve estimating,testing or predicting many things, that is, large-scale inference, the title of Bradley Efron’s latestbook. Although there are clear precursors, notably R. von Mises in 1942 studying water quality,and R. A. Fisher and colleagues in 1943 surveying butterfly species, the story presented in thisbook begins in 1956 with papers presented to the Third Berkeley Symposium by H. Robbinson an empirical Bayes approach to Statistics, and C. Stein on the inadmissibility of the usualestimator of the mean of the multivariate normal distribution. It was not, and is not immediatelyobvious that these two papers have a lot in common, much less with the theory of simultaneoushypothesis testing with linear models, and with R. A. Fisher’s butterflies. But they do, and asbest I can tell—the book is not clear on this point—the connection was made around 1974–1975by Efron himself, perhaps in collaboration with others. What was a modest sub-field of statisticstwo or three decades ago, has become much more important now that many has came to mean,not just 10 or 100, but 10 thousand or 100 thousand or more, which is where we are now.

In the last decade, Efron has played a leading role in laying down the foundations of large-scale inference, not only in bringing back and developing old ideas, but also linking them withmore recent developments, including the theory of false discovery rates and Bayes methods. Weare indebted to him for this timely, readable and highly informative monograph, a book he isuniquely qualified to write. It is not a comprehensive text on the topics in its title, for example,



some important works on empirical Bayes methods are not mentioned. Rather, it is a synthesisof many of Efron’s own contributions over the last decade with that of closely related material,together with some connecting theory, valuable comments, and challenges for the future. Hisavowed aim is “not to have the last word” but to help us deal “with the burgeoning statisticalproblems of the 21st century”. He has succeeded admirably.

Terry Speed: [email protected] of Statistics, 367 Evans Hall #3860

University of California, Berkeley, CA 94720-3860, USA

Visualizing Data Patterns with MicromapsDaniel B. Carr, Linda Williams PickleChapman & Hall/CRC, 2010, xvii + 164 pages, £44.99/$69.95, hardcoverISBN: 978-1-4200-7573-1

Table of contents

1. An introduction to micromaps2. Research influencing micromap design3. Data visualization design principles4. Linked micromaps5. Conditioned micromaps

6. Comparative micromaps7. Putting it all together

Appendix 1. Data sources and notesAppendix 2. Symmetric perceptual groupings

Readership: Scientists wishing to explore and present spatial data with maps.

Charting geographic data is difficult. Polygon map displays of data recorded by area arecommonly used, though they suffer from large areas often having tiny populations while smallareas have large populations, so that assessing spatial patterns can be tricky. Interactive software isone approach to making the displays more flexible and useful. Spatial displays called micromaps,a form of display using small multiples, have been suggested by Dan Carr, and applied anddeveloped in collaboration with Linda Pickle, primarily to US health data. Graphics like theseare immediately recognisable to people familiar with the areas shown, and the book mainly usesdata for the fifty US States plus the District of Columbia. Overall, micromaps are an effectivetool and the book explains them at length, with lots of examples, so that non-statisticians canunderstand and use them. Of course, this means that there is little statistical depth and althoughthe authors frequently and properly recommend caution in overinterpreting the displays, theyoccasionally indulge in it themselves, for instance in discussing Figure 4.15 and Figure 5.3.Dealing with graphics requires many different skills and it is a strength of the book that therelevant topics in perception and cognition are well summarised in the second chapter.

While the book is attractively presented in full colour and there are many real examples, it is abit surprising that these are not more striking. The authors have been using micromaps for manyyears and you would expect them to present their most insightful graphics in their book. Whenthey stray from the US, as in Figure 6.3 where they display yield spreads for government bondsfor a number of countries, they are not successful at all (and don’t appear to have noticed that inthe first of seven maps of the world, continental Europe and most of Asia are missing). In thefinal chapter there is a lengthy discussion of a fascinating dataset for Louisiana before and afterHurricane Katrina. Various types of micromaps are used and reveal interesting information. Insome cases other kinds of display would have been more effective and it is an opportunity missed



not to show micromaps in conjunction with other displays. There are several references to theavailability of code, maps and data on the book’s website. At the time of writing, this has notyet happened. Some excellent material is available on Dan Carr’s own website (for instance, theKatrina dataset) and elsewhere, but not all that is promised in the book.

In general the graphic displays in this book are clear and straightforward, they are notcluttered with unnecessary decoration. Reasons for poor display and how poor display maybe avoided are well covered in the second chapter. They suggested a way of presenting myfinal recommendation, which has been hidden in the layout of the review. In the form you arecurrently reading this will be difficult to spot. If you want a clue, think of the Book of Kells,and if you don’t, look at the version of the review on my website.



Statistics for Archaeologists: A Common Sense Approach, Second EditionRobert D. DrennanSpringer, 2010, xv + 333 pages, €49.94/£44.99/$49.95, softcoverISBN: 978-1-4419-6071-9

Table of contents

Part I. Numerical Exploration1. Batches of numbers2. The level or center of a batch3. The spread or dispersion of a batch4. Comparing batches5. The shape or distribution of a batch6. Categories

Part II. Sampling7. Samples and populations8. Different samples from the same population9. Confidence and population means

10. Medians and resampling11. Categories and population proportions

Part III. Relationships between Two Variables12. Comparing two sample means13. Comparing means of more than two samples

14. Comparing proportions of different samples15. Relating a measurement variable to another

measurement variable16. Relating ranks

Part IV. Special Topics in Sampling17. Sampling a population with subgroups18. Sampling a site or region with spatial units19. Sampling without finding anything20. Sampling and reality

Part V. Multivariate Analysis21. Multivariate approaches and variables22. Similarities between cases23. Multidimensional scaling24. Principal components analysis25. Cluster analysis

Readership: Archeologists and others; read the next paragraph.

“This book is intended as an introduction to basic statistical principles and techniques for thearchaeologist” says the opening of the preface. “All examples and exercises are set specificallyin the context of archaeology . . . (However) physical anthropologists, sociologists, politicalscientists and specialists in other fields make use of these same principles and techniques. Themix of topics, (and the) approach . . . reflect my own view of what is most useful . . . (for) . . .

archeological data.”For the indicated type of audience, this is a superb book, setting the use of basic statistics in a

format that makes sense of the formulas rather than just saying “compute this”. Mathematicallyfluent students who scorn a specific context will complain that there is too much “talky talky”



surrounding the formulas. That talk, missing from many applied elementary texts, is especiallywhat the audience for this book needs and deserves, and rarely gets in class, in my experience.To the mathematically well endowed, books like this can appear somewhat simple minded. Theyare, however, very hard to write.

Robert Drennan (and his wife, acknowledged in the preface) have succeeded where othershave failed, namely to explain, in an understandable way, the advantages of simple statisticaltechniques in a specific applied context. I heartily recommend this text.



Plans d’experience: constructions et analyses statistiquesWalter TinssonSpringer, 2010, xv + 532 pages, €94.79/£85.90/$129.00, brocheISBN: 978-3-642-11471-7

Table des matieres

Partie I. Generalites1. La notion de plan d’experience2. Outils mathematiques pour les plans

d’experiencePartie II. Plans d’experience pour facteurs quantitatifs

3. Plans d’experience pour modeles d’ordre un4. Plans d’experience pour modeles a effects

d’interactions5. Plans d’experience pour surfaces de reponse6. Plans d’experience en blocs7. Plans d’experience pour melanges

Partie III. Plans d’experience pour facteurs qualitatifs8. Plans d’experience pour facteurs qualitatifs9. Plans d’experience en bloc pour facteur

qualitatifsPartie IV. Optimalite des plans d’experience

10. Criteres d’optimalitePartie V. AnnexesA. Plans factoriel et representation lineaire des

groupesB. Plans d’experience classiquesC. Notations utilisees

Public vise: Statisticiens, chercheurs en plans d’experience, ingenieurs.

Ce livre se situe a mi-chemin entre les ouvrages appliques qui proposent des catalogues de plansd’experience et les ouvrages theoriques qui, en etant trop abstraits, sont difficilement exploitablespour les applications. Les nombreux exemples developpes permettent de bien comprendre lesenjeux. Par ailleurs, les outils mathematiques necessaires y sont bien detailles.

Le cœur du livre, correspondant aux chapitres de la partie II, proposent un traitement completde differentes problematiques industrielles. Le cheminement se fait en trois etapes: discussionsur le modele a utiliser, choix du plan d’experience associe et analyse statistique qui en decoule.Ce schema identique a tous ces chapitres permet d’avoir une vision coherente des sujets traites.Par ailleurs, les outils mathematiques necessaires y sont bien detailles et le lecteur qui souhaitentapprofondir les details les plus techniques trouvera a la fin de chaque chapitre de nombreuxdeveloppements.

L’auteur a choisi de se concentrer sur les proprietes d’orthogonalite pour justifier le choix desplans d’experience utilises, alors que l’efficacite et les proprietes d’optimalite des plans ne sontevoques qu’au dernier chapitre du livre ce qui nuit un peu a la vision d’ensemble. On noteral’absence d’exemple d’utilisation de logiciels dedies a la construction de plans d’experienceainsi que du traitement des modeles non-linaires.



En conclusion, ce livre est ideal pour les etudiants en master de statistique ou les ingenieursen activite ayant a utiliser les plans d’experience.

Pierre Druilhet: [email protected] Blaise Pascal, Laboratoire de Mathematiques

Campus des Cezeaux, B.P. 80026, 63177 Aubiere cedex, France

Bayesian Analysis for Population EcologyRuth King, Byron J. T. Morgan, Olivier Gimenez, Stephen P. BrooksChapman & Hall/CRC, 2010, xiii + 442 pages, £50.99/$82.95, hardcoverISBN: 978-1-4398-1187-0

Table of contents

Part I. Introduction to Statistical Analysis ofEcological Data

1. Introduction2. Data, models and likelihoods3. Classical inference based on the likelihood

Part II. Bayesian Techniques and Tools4. Bayesian inference5. Markov Chain Monte Carlo6. Model discrimination

7. MCMC and RJMCMC computer programsPart III. Ecological Applications

8. Covariates, missing values and random effects9. Multi-state models

10. State-space modelling11. Closed populations

Appendix A: Common distributionsAppendix B: Programming in RAppendix C: Programming in WinBUGS

Readership: Ecologists interested in Bayesian Analysis of Ecological problem, also otherecologists in general, who are interested in any of the following, population ecological modelsand statistical inference based on those models and classical or Bayesian methods.

The book is divided into three parts. The first part introduces some general problems ofpopulation ecology and a rich collection of models to solve these problems via likelihood basedclassical inference. Likelihoods are easy to derive once one has well defined data collectionprocedures and probability models for the data.

One class of major general problems is the study of extinction, abundance or runaway growthof different species. To answer this, one has to estimate the population total in each populationfor several years. Depending on the species under consideration, one may have a census, or theCommon Bird Census or data based on marked samples which are then partly recaptured insubsequent samples. Each method will have its own model and likelihood and likelihood basedestimate and so on. Even the technique of marking animals differs widely from population topopulation. Birds are ringed, insects are marked by specks of fat, animals may be marked byradio transmitters and tracked by satellite. Even DNA matching is used in some cases. Part 1contains a wealth of material on aspect of such data, models analysis as well as the history ofevolution of the subject.

Part 2 is a good, self-contained introduction to Bayesian Analysis for the problems mentionedabove. There are good discussions of informative and not so informative priors, the Jeffreys prior,different techniques of MCMC, including Gibbs sampling, Metropolis–Hastings algorithm, andthe Reversible Jump MCMC for model selection or calculation of posterior distribution ofparameters given a model. It appears that the ease with which Bayesians can average overmodels or choose a model in a well calibrated way has been one of the main reasons forpopularity of Bayesian methods in ecology.



Part 3 is a collection of interesting special topics in ecological applications. They includemissing values, state space models (without the usual linearity and normal distribution), andapplications of model fitting, model choice and model average.

The authors write very well and illustrate with good examples. Both the technical and non-technical discussions are good.

Jayanta K. Ghosh: [email protected] of Statistics, Purdue University

West Lafayette, IN 47909, USA

NIST Handbook of Mathematical FunctionsFrank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark (Editors)Cambridge University Press, 2010, xv + 951 pages, £35.00/$50.00, softcover (also available ashardcover)ISBN: 978-0-521-14063-8

Table of contents

1. Algebraic and analytic methods (Ranjan Roy,Frank W. J. Olver, Richard A. Askey, RoderickS. C. Wong)

2. Asymptotic approximations (Frank W. J. Olver,Roderick S. C. Wong)

3. Numerical methods (Nico M. Temme)4. Elementary functions (Ranjan Roy, Frank W. J.

Olver)5. Gamma function (Richard A. Askey, Ranjan

Roy)6. Exponential, logarithmic, sine and cosine

integrals (Nico M. Temme)7. Error functions, Dawson’s and Fresnel integrals

(Nico M. Temme)8. Incomplete gamma and related functions

(Richard B. Paris)9. Airy and related functions (Frank W. J. Olver)

10. Bessel functions (Frank W. J. Olver, Leonard C.Maximon)

11. Struve and related functions (Richard B. Paris)12. Parabolic cylinder functions (Nico M. Temme)13. Confluent hypergeometric functions (Adri B.

Olde Daalhuis)14. Legendre and related functions (T. Mark

Dunster)15. Hypergeometric function (Adri B. Olde

Daalhuis)16. Generalized hypergeometric functions and

Meijer G-function (Richard A. Askey, Adri B.Olde Daalhuis)

17. q-Hypergeometric and related functions

(George E. Andrews)18. Orthogonal polynomials (Tom H. Koornwinder,

Roderick S. C. Wong, Roelof Koekoek, Rene F.Swarttouw)

19. Elliptic integrals (Bille C. Carlson)20. Theta functions (William P. Reinhardt, Peter L.

Walker)21. Multidimensional theta functions (Bernard

Deconinck)22. Jacobian elliptic functions (William P.

Reinhardt, Peter L. Walker)23. Weierstrass elliptic and modular functions

(William P. Reinhardt, Peter L. Walker)24. Bernoulli and Euler polynomials (Karl Dilcher)25. Zeta and related functions (Tom M. Apostol)26. Combinatorial analysis (David M. Bressoud)27. Functions of number theory (Tom M. Apostol)28. Mathieu functions and Hill’s equation

(Gerhard Wolf )29. Lame functions (Hans Volkmer)30. Spheroidal wave functions (Hans Volkmer)31. Heun functions (Brian D. Sleeman, Vadim

Kuznetsov)32. Painleve transcendents (Peter A. Clarkson)33. Coulomb functions (Ian J. Thompson)34. 3j,6j,9j symbols (Leonard C. Maximon)35. Functions of matrix argument (Donald St. P.

Richards)36. Integrals with coalescing saddles (Michael V.

Berry, Chris Howls)

Readership: Mathematicians, scientists (theoretical physicists, engineers, chemists, statisticians,economists, etc.).



This is like trying to review the bible: it would be eccentric to argue that it is not a “thoroughlygood thing”. It’s the modern successor to the wonderful Handbook of Mathematical Functions,edited by Abramowitz and Stegun, and maybe that’s enough said.

However, a few aspects deserve comment. The Preface tells us that this has been a ten-yearproject, involving many technical experts both within and without the NIST. Major developmentsinclude:

(i) the omission of tables of values of special functions, previously listed in Abramowitz andStegun;

(ii) the introduction of full-colour graphics;(iii) a list of applications of the special functions in each chapter;(iv) the availability of a web-based version.

In place of (i) there is now a Computation section in each chapter: available methods aredescribed, references are given, and links to sites where software can be accessed are identified.With (ii) one can see at a glance how the function behaves, a picture painting a thousand words,as they say. Feature (iii) might sometimes help to introduce new ways of looking at a particularfunction. Facility (iv) is likely to become an everyday tool of many researchers: the online versionis the NIST Digital Library of Mathematical Functions (DLMF), accessible at . In addition thereis a CD in a pocket at the back with the whole book in a pdf file.

In summary, this splendid work doesn’t really need the approbation of a mere reviewer. Andnow I’m off to look up my first unidentified integral to see if it’s a standard form.

Martin Crowder: [email protected] Department, Imperial College

London SW7 2AZ, UK

Hidden Markov Models for Time Series: An Introduction Using R, Second EditionWalter Zucchini, Iain L. MacDonaldChapman & Hall/CRC, 2009, xxii + 275 pages, £50.99/$82.95, hardcoverISBN: 978-1-58488-573-3

Table of contents

Part One: Model Structure, Properties and Methods1. Preliminaries: mixtures and Markov chains2. Hidden Markov models: definition and

properties3. Estimation by direct maximization of the

likelihood4. Estimation by the EM algorithm5. Forecasting, decoding and state prediction6. Model selection and checking7. Bayesian inference for Poisson-HMMs8. Extensions of the basic hidden Markov model

Part Two: Applications9. Epileptic seizures

10. Eruptions of the Old Faithful geyser11. Drosophila speed and change of direction12. Wind direction at Koeberg13. Models for financial series14. Births at Edendale hospital15. Homicides and suicides in Cape Town16. Animal behavior model with feedback

Appendix A: Examples of R codeAppendix B: Some proofs

Readership: Applied statisticians, scientists, engineers, users of Statistics.

This is by way of a follow-up to the authors’ previous book in 1997. There, the time seriesconsidered were discrete-valued: Part I (50 pages) presented a survey of models, and Part II(150 pages) concentrated on hidden Markov models. In this new book, the old Part I has been



removed, which is a slight shame, since it covered an interesting variety of models: the authorsreason that such models have not been used widely in applications. Instead, the treatment is nowextended to cover continuous as well as discrete-valued data.

In this 2009 book data of many types are considered, including binary, categorical, counts,continuous (univariate and multivariate) and circular. The authors point out that their bookplaces emphasis on applications rather than theoretical research, and mention others moresuitable for readers interested in the latter. Indeed, Part II comprises over 100 pages devoted toeight applications, one per chapter. The data are available for download from a web site andR-code for performing the analyses is listed in Appendix A. Nevertheless, the mathematicalunderpinning for the models is set out clearly in Part I (132 pages). Here the basic definition andproperties of hidden Markov chains are covered, together with computational details, inference,prediction, model-checking, and some extensions.

It is clear that much care has gone into this book: it has a very detailed contents list, a list ofabbreviations and notations, thoughtful data analyses, many references and a detailed index. Infact, it would be difficult not to thoroughly recommend it to anyone interested in learning howto tackle these types of data.


London SW7 2AZ, UK



Meta-analysis and Combining Information in Genetics and GenomicsRudy Guerra, Darlene R. Goldstein (Editors)Chapman & Hall/CRC, 2010, xxiii + 335 pages, £63.99/$99.95, hardcoverISBN: 978-1-58488-522-1

Table of contents

Part 0. Introductory Material1. A brief introduction to meta-analysis, genetics

and genomics (Darlene R. Goldstein, RudyGuerra)

Part I. Similar Data Types I: Genotype Data2. Combining information across genome-wide

linkage scans (Carol J. Etzel, Tracy J. Costello)3. Genome search meta-analysis (GSMA): a

nonparametric method for meta-analysis ofgenome-wide linkage studies (Cathryn M.Lewis)

4. Heterogeneity in meta-analysis of quantitativetrait linkage studies (Hans C. vanHouwelingen, Jeremie J. P. Lebrec)

5. An empirical Bayesian framework for QTLgenome-wide scans (Kui Zhang, HowardWiener, T. Mark Beasley, Christopher I. Amos,David B. Allison)

Part II. Similar Data Types II: Gene Expression Data6. Composite hypothesis testing: an approach

built on intersection-union tests and Bayesianposterior probabilities (Stephen Erickson,Kyoungmi Kim, David B. Allison)

7. Frequentist and Bayesian error poolingmethods for enhancing statistical power insmall sample microarray data analysis (Jae K.Lee, Hyung Jun Cho, Michael O’Connell)

8. Significance testing for small microarrayexperiments (Charles Kooperberg, AaronAragaki, Charles C. Carey, SuzannahRutherford)

9. Comparison of meta-analysis to combinedanalysis of a replicated microarray study(Darlene R. Goldstein, Mauro Delorenzi, RuthLuthi-Carter, Thierry Sengstag)

10. Alternative probe set definitions for combiningmicroarray data across studies using differentversions of Affymetrix oligonucleotide arrays(Jeffrey S. Morris, Chunlei Wu, Kevin R.Coombes, Keith A. Baggerly, Jing Wang, LiZhang)

11. Gene ontology-based meta-analysis ofgenome-scale experiments (Chad A. Shaw)

Part III. Combining Different Data Types12. Combining genomic data in human studies

(Debashis Ghosh, Daniel Rhodes, ArulChinnaiyan)

13. An overview of statistical approaches forexpression trait loci mapping (ChristinaKendziorski, Meng Chen)

14. Incorporating GO annotation information inexpression trait loci mapping (J. BlairChristian, Rudy Guerra)

15. A misclassification model for inferringtranscriptional regulatory networks (Ning Sun,Hongyu Zhao)

16. Data integration for the study of proteininteractions (Fengzhu Sun, Ting Chen,Minghua Deng, Hyunju Lee, Zhidong Tu)

17. Gene trees, species trees, and species networks(Luay Nakhleh, Derek Ruths, Hideki Innan)

Readership: Students and researchers in meta-analysis of biological data.

The theme is the pooling of information from a number of distinct data sets, specifically genomicdata. The current statistical methodology for this purpose falls under the umbrella term meta-analysis. The stated aim of this book is to contribute to the development of such techniquesto a wider and more diverse area of applications. This is in response to the rapidly increasingproduction of large amounts of genomic data of various types.

This is an edited volume of 17 chapters contributed jointly by 45 subject experts. There isan introductory chapter, setting out the framework and giving a brief survey of the basic ideasand methods. There follow 16 chapters dealing with a variety of more specialised areas ofapplication. These are organised into three parts: Parts I and II address the treatment of differentsets of data of similar type; Part III extends this to data of different types. The chapters are largelyself-contained, so that readers can dip in to the particular articles of interest to themselves.

The book assumes a certain level of mathematical and statistical experience. Familiaritywith probability manipulation and distributions, together with a working knowledge of standard



statistical inference and methods, is presumed. However, the editors point out that the moretechnical parts can be glossed over if the reader wishes.

My impression is that the book will be most useful for students and researchers who wishto see what developments are currently in progress in this important area. That said, there isa wealth of material here for the non-expert wishing to move into the area. And, unlike someedited tomes in past ages, the articles here have clearly been carefully meshed to give a coherentpicture.


London SW7 2AZ, UK

Diagnostic Measurement: Theory, Methods, and ApplicationsAndre A. Rupp, Jonathan Templin, Robert A. HensonGuilford Press, 2010, xx + 348 pages, $75.00, hardcover (also available as softcover)ISBN: 978-1-60623-528-7

Table of contents

1. IntroductionPart I. Theory: Principles of Diagnostic Measurement

with DCMs2. Implementation, design, and validation of

diagnostic assessments3. Diagnostic decision making with DCMs4. Attribute specification for DCMs

Part II. Methods: Psychometric Foundations of DCMs5. The statistical nature of DCMs6. The statistical structure of core DCMs

7. The LCDM framework8. Modeling the attribute space in DCMs

Part III. Applications: Utilizing DCMs in Practice9. Estimating DCMs using Mplus

10. Respondent parameter estimation in DCMs11. Item parameter estimation in DCMs12. Evaluating the model fit of DCMs13. Item discrimination indices for DCMs14. Accommodating complex sampling designs in

DCMs

Readership: Students, educators, scientists from applied statistics, psychometrics, measurementand research methodology, psychological and educational assessment, and other areas.

This book focuses on what the authors call “diagnostic classification models” (DCMs): “aparticular subset of psychometric models that yield classifications of respondents accordingto multiple latent variables,” (their italics). The generality of that description means that it isnot surprising that the roots of such models have also been explored in other classes of modelswhich might be more familiar, including classical test theory, item response theory, confirmatoryfactor analysis, structural equation modelling, and categorical data analysis. The authors say theychose the term “diagnostic classification model” to emphasise that, although DCMs are statisticaltools, a theory about response processes grounded in applied cognitive psychology is desirablein practical applications. The book by Skrondal and Rabe-Hesketh (2004) Generalized LatentVariable Modeling covers similar topics from a more overtly statistical perspective.

The book is divided into three parts covering, respectively, the theory, methods, andapplications of DCMs, with the theory part essentially setting the context and framework forsuch models. The methods section describes the sorts of statistical modelling tools used, coveringsuch as log-linear models, latent class models, and Bayesian networks, and in fact, in Chapter 7the authors show that core DCMs can be expressed in a log-linear modelling framework.

The applications part of the book is not so much a collection of illustrative applications as anelaboration of the methods part, looking at topics such as estimation, model fit, and complex



sample designs. However, the book does include examples, and these are demonstrated using theMplus system, a software package based around latent variables. Although there are no exercisesin the book, the preface does say that exercises and solutions will be given on the associatedwebsite (though when I tried, I was unable to get past the main page, but I imagine that was apassing aberration.)

Given its central emphasis on diagnosis, I was a little surprised that the description of standardmeasures of model fit given in Chapter 12 was not complemented by some discussion of theparallel literature on evaluating the performance of diagnostic rules in cases when the truediagnoses can (perhaps subsequently) be discovered. This literature is now vast – see, forexample, Zhou, Obuchowski, and McLish (2002) Statistical Methods in Diagnostic Medicineand Pepe (2003) The Statistical Evaluation of Medical Tests for Classification and Prediction.Perhaps routes into this related literature might be added in a second edition.


London SW7 2AZ, UK

Biplots in PracticeMichael GreenacreFundacion BBVA, 2010, 237 pages, €32.00, softcoverISBN: 978-84-923846-8-6

Table of contents

1. Biplots—the basic idea2. Regression biplots3. Generalized linear model biplots4. Multidimensional scaling biplots5. Reduced-dimension biplots6. Principal component analysis biplots7. Log-ratio biplots8. Correspondence analysis biplots9. Multiple correspondence analysis biplots I

10. Multiple correspondence analysis biplots II11. Discriminant analysis biplots

12. Constrained biplots and triplots13. Case study 1—biomedicine: comparing cancer

types according to gene expression arrays14. Case study 2—socio-economics: positioning

the “middle” category in survey research15. Case study 3—ecology: the relationship

between fish morphology and dietAppendix A: Computation of biplotsAppendix B: BibliographyAppendix C: Glossary of termsAppendix D: Epilogue

Readership: Researchers and students of both social and natural sciences interested in learningmore about multivariate data visualization.

First of all, I am happy to say that Michael Greenacre has written an extremely useful book!Although the technique of biplots has been known for about 40 years, it has not yet become

a widely applied method, with the exception of correspondence analysis and related methods,where it is absolutely crucial for presenting any results graphically. In general, the aim of biplotis to visualize the maximum possible amount of information in the multivariate data. That soundslike a typical aim in quite many other circumstances as well. Therefore I believe that biplots willeventually become a popular technique in several new fields.

Before this book, there have not been too many books about biplots, or perhaps they have beena bit too theoretical for most applications. Now, this book explains very clearly what biplots are,how they are constructed and how they are used and interpreted in various applications, both insocial and natural sciences.



Twelve chapters go smoothly through the basics and generalizations of biplots in connectionwith various statistical methods, such as multidimensional scaling, principal componentsanalysis, correspondence analysis, and discriminant analysis. They are followed by threeexcellent case studies from different fields, demonstrating very well the possibilities of biplotsin practice.

The computational aspects are explained in an appendix and on the website of the book,although some R code is also given within the chapters, when it is necessary to clarify someparticular details.

In all, the book is easy to read, because it follows a didactic format, with many nice figuresand tables, chapter summaries, a glossary of terms, an annotated bibliography and everything. Ifeel that this book really supports learning! I have already used it on my course, which is easy,as the whole book is also freely available on its website.

Kimmo Vehkalahti: [email protected] of Social Research, StatisticsFI-00014 University of Helsinki, Finland

Regression Modeling with Actuarial and Financial ApplicationsEdward W. FreesCambridge University Press, 2010, xvii + 565 pages, £35.00/$56.99, softcover (also availableas hardcover)ISBN: 978-0-521-13596-2

Table of contents

1. Regression and the normal distributionPart I. Linear Regression

2. Basic linear regression3. Multiple linear regression—I4. Multiple linear regression—II5. Variable selection6. Interpreting regression results

Part II. Topics in Time Series7. Modeling trends8. Autocorrelations and autoregressive models9. Forecasting and time series models

10. Longitudinal and panel data modelsPart III. Topics in Nonlinear Regression

11. Categorical dependent variables12. Count dependent variables

13. Generalized linear models14. Survival models15. Miscellaneous regression topics

Part IV. Actuarial Applications16. Frequency-severity models17. Fat-tailed regression models18. Credibility and bonus-malus19. Claims triangles20. Report writing: communicating data analysis

results21. Designing effective graphs

Appendix 1: basic statistical inferenceAppendix 2: matrix algebraAppendix 3: probability tables

Readership: Academic: researcher and graduate students in applied mathematics, statistics andapplied finance; Industry: Actuaries and risk management professionals. The book assumesknowledge comparable to a one-semester introduction to probability and statistics.

This is an excellent book written by an all-round writer. He is a Fellow of both the Society ofActuaries and the American Statistical Association. Hence, it is not surprising that the bookfills the gap between modern statistics and traditional actuarial/risk management methods.Need for this kind of book is obvious. As Jukka Rantala—the former Chairman of GroupeConsultatif (European Actuarial Association)—stated, practicing actuaries will benefit fromclose co-operation between practice and research; in particular statistics.



This book presents an overview of how statistics can be used to solve problems in actuarialand financial applications. The depth of the topics covered varies from elementary to fairlyadvanced ones.

The book describes applications of regression methods to important actuarial problems. Theauthor has chosen topics that have been relevant in his research and consultation work, thatis, Bonus-Malus systems and claim triangles. The material is supported by exercises towardspractical applications and a companion webpage containing datasets and SAS/R scripts.

This book has been developed as a textbook but it can also be used for self-study or as areference material for an “armchair actuary” who only passively reads. I highly recommend itto any person who wishes to learn how to use statistical methods for actuarial and financialapplications.

Lasse Koskinen: [email protected] Finnish Financial Supervisory Authority

P.O. Box 103, FI-00101 Helsinki, Finland

Creative Minds, Charmed Lives: Interviews at Institute for Mathematical Sciences,National University of SingaporeYu Kiang Leong (Editor)World Scientific, 2010, xv + 333 pages, £48.00/$78.00, hardcoverISBN: 978-981-4317-58-0

Table of contents

1. Bela Bollobas: Graphs Extremal and Random2. Leonid Bunimovich: Stable Islands, Chaotic

Seas3. Tony Fan-Cheong Chan: On Her Majesty’s (the

Queen of Science’s) Service4. Sun-Yung Alice Chang: Analyst in Conformal

Land5. Jennifer Tour Chayes: Basic Research, Hidden

Returns6. Carl de Boor: On Wings of Splines7. Persi Diaconis: The Lure of Magic and

Mathematics8. David Donoho: Sparse Data, Beautiful Mine9. Robert F. Engle: Archway to Nobel

10. Hans Follmer: Efficient Markets, RandomPaths

11. Avner Friedman: Mathematician in Control12. Roe Goodman: Mathematics, Music, Masters13. Bryan T. Grenfell: Viral Visitations, Epidemic

Models14. Takeyuki Hida: Brownian Motion, White Noise15. Roger Howe: Exceptional Lie Group Theorist16. Wilfrid Kendall: Dancing with Randomness17. Lawrence Klein: Economist for All Seasons18. Brian E. Launder: Modeling and Harnessing

Turbulence19. Fanghua Lin: Revolution, Transitions, Partial

Differential Equations20. Pao Chuen Lui: Of Science in Defense

21. Eric Maskin: Game Theory Master22. Eduardo Massad: Infectious Diseases,

Vaccines, Models23. Daniel McFadden: Choice Models, Maximal

Preferences24. Keith Moffatt: Magnetohydrodynamic

Attraction25. Stanley Osher: Mathematician with an Edge26. Doug Roble: Computer Vision, Digital Magic27. Ron Shamir. Unraveling Genes, Understanding

Diseases28. Albert Nikolaevich Shiryaev: On the Shoulder

of a Giant29. David O. Siegmund: Change-Point, a

Consequential Analysis30. Theodore Slaman and W. Hugh Woodin: Logic

and Mathematics31. Terry Speed: Good Gene Hunting32. Charles Stein: The Invariant, the Direct and the

“Pretentious”33. Gilbert Strang: The Changing Face of Applied

Mathematics34. Eitan Tadmor: Zen of Computational Attraction35. Michael Todd: Optimization, an Interior Point

of View36. Sergio Verdu: Wireless Communications, at the

Shannon Limit37. Michael S. Waterman: Breathing Mathematics

into Genes



Readership: Mathematicians, statisticians, mathematical scientists, historians of mathematics,historians of ideas, students and general public.

This interview volume is a collection of all the interviews of prominent visitors to the Institutefor Mathematical Sciences, National University of Singapore, conducted by Yu Kiang Leongand published in the Institute’s newsletter Imprints from 2003 to 2009.

In the Preface the Editor writes as follows: “Research papers very rarely give any inklingas to how an important idea was conceived; the crucial idea is almost always presented as if itappeared out of the blue in its final form to the discoverer. If he or she could be persuaded duringan interview to shed some light on the process that led to the discovery of the idea, it would havebeen worth the interview.” I am happy to congratulate the Editor for his reaching the goal: thisis a very well prepared collection of views of influential mathematical scientists. Nicely printed,great photographs! Students considering possible academic career, would certainly enjoy findingthe human persons behind the famous names—some almost legends.

— If a graduate student has to choose a field of research, what kind of advice would you givehim?— What led you into formatting the innovative ARCH model?— Do you think that there is still a gap in communication, if not in interaction, between themajority of economists and the majority of mathematicians?— It is often said that this century will be the century of molecular biology. In your opinion,how much of this is hype and how much of it is scientifically justified?

If you are interested in learning the replies of Persi Diaconis, Robert F. Engle, Lawrence Klein,and Terry Speed to these questions, please take a look at Creative Minds, Charmed Lives.

Simo Puntanen: [email protected] of Information Sciences

FI-33014 University of Tampere, Finland

Design of Experiments: An Introduction Based on Linear ModelsMax D. MorrisChapman & Hall/CRC, 2011, xviii + 355 pages, £39.99/$89.95, hardcoverISBN: 978-1-58488-923-6

Table of contents

1. Introduction2. Linear statistical models3. Completely randomized designs4. Randomized complete blocks and related

designs5. Latin squares and related designs6. Some data analysis for CRDs and orthogonally

blocked designs7. Balanced incomplete block designs8. Random block effects9. Factorial treatment structure

10. Split-plot designs

11. Two-level factorial experiments: basics12. Two-level factorial experiments: blocking13. Two-level factorial experiments: fractional

factorials14. Factorial group screening experiments15. Regression experiments: first-order polynomial

models16. Regression experiments: second-order

polynomial models17. Introduction to optimal design

Appendix A: Calculations using RAppendix B: Solution notes for selected exercises



Readership: Graduate or advanced undergraduate statisticians and experienced practitioners.

This book discusses experimental design with a strong emphasis on linear models. Althoughwith a very pragmatic and a practitioner-oriented point of view, this book is intended fora thorough and deeper introduction to experimental design. It dwells with the derivation ofestimates, decomposition of error, precision and sample size (among other issues) for each classof classical experimental designs. It also introduces some more advanced concepts, namely thevarious types of optimality for an experimental design.

The first chapter deals with the basic concepts of creating an experiment. It starts withthe notions of experimental unit, treatment, block and other basic notions. The concept ofrandomization, control and information are also treated.

The second chapter is a keystone in the book, since it deals with the theory of linear models.Estimation in both a simple and partitioned models is treated, as well as the calculation ofthe information associated to designs. Orthogonality conditions and hypothesis testing on themodel’s parameters is also covered.

The three following chapters describe completely randomized designs (CRD), randomizedcomplete block designs (RCBD), Latin squares and related models are treated. A data-drivenexample is always presented, followed by the linear model that describes it. Besides the usualestimation and analytical approach, a graphical analysis is made. Efficiency and precision iscalculated for each model, with comparisons between families of models are made.

The two subsequent chapters treat data analysis, model assumption tests and treatmentcomparison for the above mentioned models. Next, balanced incomplete block designs andrelated models are treated. Like with the previously mentioned model classes, examples, modelformulation, analysis and efficiency is covered as well as conditions for the existence of thesedesigns. Random effects for blocks is considered and presented, with intra and inter-blockestimation and inter-block information recovery. Application of these techniques to the beforediscussed models is presented and discussed.

Chapter 9 discusses the general structure of factorial models, presenting the general frameworkfor this class of models. In subsequent chapters (11, 12 and 13) the base 2 factorial is presentedin detail, followed by blocking and fractional replication for this sub-class of factorial models.Split-plot models are discussed in chapter 10.

The last four chapters deal with more advanced subjects. Chapter 14 studies factorial screening,when the number of binary factors in experiment is large and factor group significance needsto be inferred. Chapters 15 and 16 analyze polynomial regression models of first and secondorder, respectively. Analysis and experiment design using these models is made. The last chapterpresents a brief introduction to optimality.

Miguel Fonseca: [email protected] of Mathematics and Applications

Faculty of Sciences and Technology, New University of Lisbon2829-516 Caparica, Portugal



Algorithms and Theory of Computation Handbook, Second Edition—2 Volume SetMikhail J. Atallah, Marina Blanton (Editors)Chapman & Hall/CRC, 2010, xv + 988 and xvi + 950 pages, £119.00/$185.95, hardcoverISBN: 978-1-58488-818-5

Table of contents

Volume 1: General Concepts and Techniques1. Algorithm design and analysis techniques

(Edward M. Reingold)2. Searching (Ricardo Baeza-Yates, Patricio V.

Poblete)3. Sorting and order statistics (Vladimir

Estivill-Castro)4. Basic data structures (Roberto Tamassia, Bryan

Cantrill)5. Topics in data structures (Giuseppe F. Italiano,

Rajeev Raman)6. Multidimensional data structures for spatial

applications (Hanan Samet)7. Basic graph algorithms (Samir Khuller, Balaji

Raghavachari)8. Advanced combinatorial algorithms (Samir

Khuller, Balaji Raghavachari)9. Dynamic graph algorithms (Camil Demetrescu,

David Eppstein, Zvi Galil, Giuseppe F.Italiano)

10. External memory algorithms and datastructures (Lars Arge, Norbert Zeh)

11. Average case analysis of algorithms (WojciechSzpankowski)

12. Randomized algorithms (Rajeev Motwani,Prabhakar Raghavan)

13. Pattern matching in strings (MaximeCrochemore, Christophe Hancart)

14. Text data compression algorithms (MaximeCrochemore, Thierry Lecroq)

15. General pattern matching (Alberto Apostolico)16. Computational number theory (Samuel S.

Wagstaff, Jr.)17. Algebraic and numerical algorithms (Ioannis Z.

Emiris, Victor Y. Pan, Elias P. Tsigaridas)18. Applications of FFT and structured matrices

(Ioannis Z. Emiris, Victor Y. Pan)19. Basic notions in computational complexity

(Tao Jiang, Ming Li, Bala Ravikumar)20. Formal grammars and languages (Tao Jiang,

Ming Li, Bala Ravikumar, Kenneth W. Regan)21. Computability (Tao Jiang, Ming Li, Bala

Ravikumar, Kenneth W. Regan)22. Complexity classes (Eric Allender, Michael C.

Loui, Kenneth W. Regan)23. Reducibility and completeness (Eric Allender,

Michael C. Loui, Kenneth W. Regan)24. Other complexity classes and measures (Eric

Allender, Michael C. Loui, Kenneth W. Regan)

25. Parameterized algorithms (Rodney G. Downey,Catherine McCartin)

26. Computational learning theory (Sally A.Goldman)

27. Algorithmic coding theory (Atri Rudra)28. Parallel computation: models and complexity

issues (Raymond Greenlaw,H. James Hoover)

29. Distributed computing: a glimmer of a theory(Eli Gafni)

30. Linear programming (Vijay Chandru, M. R.Rao)

31. Integer programming (Vijay Chandru, M. R.Rao)

32. Convex optimization (Florian Jarre, StephenA. Vavasis)

33. Simulated annealing techniques (Albert Y.Zomaya, Rick Kazman)

34. Approximation algorithms for NP-hardoptimization problems (Philip N. Klein, NealE. Young)

Volume 2: Special Topics and Techniques1. Computational geometry I (D. T. Lee)2. Computational geometry II (D. T. Lee)3. Computational topology (Afra Zomorodian)4. Robot algorithms (Konstantinos Tsianos, Dan

Halperin, Lydia Kavraki, Jean-ClaudeLatombee)

5. Vision and image processing algorithms(Concettina Guerra)

6. Graph drawing algorithms (Peter Eades,Carsten Gutwenger, Seok-Hee Hong, PetraMutzel)

7. Algorithmics in intensity-modulated radiationtherapy (Danny Z. Chen, Chao Wang)

8. VLSI layout algorithms (Andrea S. LaPaugh)9. Cryptographic foundations (Yvo Desmedt)

10. Encryption schemes (Yvo Desmedt)11. Cryptanalysis (Samuel S. Wagstaff, Jr.)12. Crypto topics and applications I (Jennifer

Seberry, Chris Charnes, Josef Pieprzyk, ReiSafavi-Naini)

13. Crypto topics and applications II (JenniferSeberry, Chris Charnes, Josef Pieprzyk, ReiSafavi-Naini)

14. Secure multiparty computation (Keith B.Frikken)

15. Voting schemes (Berry Schoenmakers)16. Auction protocols (Vincent Conitzer)

International Statistical Review (2011), 79, 1, 114–143C© 2011 The Author. International Statistical Review C© 2011 InternationalStatistical Institute.


17. Pseudorandom sequences and stream ciphers(Andrew Klapper)

18. Theory of privacy and anonymity (ValentinaCiriani, Sabrina De Capitani di Vimercati,Sara Foresti, Pierangela Samarati)

19. Database theory: query languages (NicoleSchweikardt, Thomas Schwentick, LucSegoufin)

20. Scheduling algorithms (David Karger, CliffStein, Joel Wein)

21. Computational game theory: an introduction(Paul G. Spirakis, Panagiota N. Panagopoulou)

22. Artificial intelligence search algorithms(Richard E. Korf )

23. Algorithmic aspects of natural languageprocessing (Mark-Jan Nederhof, Giorgio Satta)

24. Algorithmic techniques for regular networks ofprocessors (Russ Miller, Quentin F. Stout)

25. Parallel algorithms (Guy E. Blelloch, Bruce M.Maggs)

26. Self-stabilizing algorithms (Sebastien Tixeuil)27. Theory of communication networks (Gopal

Pandurangan, Maleq Khan)28. Network algorithmics (George Varghese)29. Algorithmic issues in grid computing (Yvers

Robert, Frederic Vivien)30. Uncheatable grid computing (Wenliang Du,

Mummoorthy Murugesan, Jing Jia)31. DNA computing: a research snapshot (Lila

Kari, Kalpana Mahalingam)32. Computational systems biology (T. M. Murali,

Srinivas Aluru)33. Pricing algorithms for financial derivatives

(Ruppa K. Thulasiram, ParimalaThulariraman)

Readership: Computer professionals and engineers.

The developments and applications in the design and analysis of algorithms continue to evolveand emerge at an ever increasing pace. Keeping abreast of new research and published work isnot a trivial task. The authors in editing the current text present a compilation that will appeal toprofessionals and students alike; together with those engaged in research and especially thosecontemplating embarking upon research.

The field has expanded substantially since the first edition appeared and has resulted inthe current two-volume format. This second edition contains twenty-one new chapters; and athorough updating and revision of many of the chapters from the first edition. A consistent stylehas been adopted but a common format has not been possible for each chapter. This does notdetract from the usefulness of the text and the sections detailing research issues and sources forfurther information will ensure that this edition remains an excellent reference source for yearsto come. I recommend this text as both a teaching aid and a reference source whose utility canonly but increase in the coming years.

Carl M. O’Brien: [email protected] for Environment, Fisheries & Aquaculture Science

Pakefield Road, Lowestoft, Suffolk NR33 0HT, UK



Stochastic Control and Mathematical Modeling: Applications in EconomicsHiroaki MorimotoCambridge University Press, 2010, xiii + 325 pages, £70.00/$110.00, hardcoverISBN: 978-0-521-19503-4

Table of contents

Part I. Stochastic Calculus and Optimal ControlTheory

1. Foundations of stochastic calculus2. Stochastic differential equations: weak

formulation3. Dynamic programming4. Viscosity solutions of

Hamilton–Jacobi–Bellman equations5. Classical solutions of

Hamilton–Jacobi–Bellman equationsPart II. Applications to Mathematical Models in

Economics6. Production planning and inventory7. Optimal consumption/investment models8. Optimal exploitation of renewable resources

9. Optimal consumption models in economicgrowth

10. Optimal pollution control with long-runaverage criteria

11. Optimal stopping problems12. Investment and exit decisions

Part III. AppendicesA. Dini’s theoremB. The Stone–Weierstrass theoremC. The Riesz representation theoremD. Rademacher’s theoremE. Vitali’s covering theoremF. The area formulaG. The Brouwer fixed point theoremH. The Ascoli–Arzela theorem

Readership: Graduate students and scientists in applied mathematics, economics, and engineer-ing theory.

What is the optimal magnitude of a choice variable at each time in a dynamical system undercertainty? In addressing this fundamental question the author, in his mathematical treatise,provides the reader with a description of stochastic control theory and its applications to dynamicoptimization. Applications in economics, mathematical finance and engineering are covered ina highly readable, and technical, style.

The text is self-contained with the necessary mathematical requisites contained in thepreliminary chapters and in the appendices. The topic of the text is one that will appeal tothose engaged in theoretical research, and is appropriate both for private study and for taughtcourses.

As the title indicates, the author’s presentation is clearly focussed on economics and providesneither exercises nor questions for further investigation. However, the chapters should allow thereader to identify future research areas. As such the text has much to commend it and the timetaken to understand the material presented will reap benefits. For those interested in theoreticalexpositions, this is a text that I can recommend.

Carl M. O’Brien: [email protected] for Environment, Fisheries & Aquaculture Science

Pakefield Road, Lowestoft, Suffolk NR33 0HT, UK


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Plans d’expérience: constructions et analyses statistiques by Walter Tinsson