de Leeuw, Jan

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Journal of Statistical Software

JSS Journal of Statistical SoftwareMarch 2007, Volume 19, Book Review 1. http://www.jstatsoft.org/Reviewer: Jan de LeeuwUniversity of California at Los AngelesComputational StatisticsGeof H. Givens and Jennifer A. HoetingWiley-Interscience, Hoboken, NJ, 2005.ISBN 0-471-46124-5. 418 pp. USD 99.95 (P).http://www.stat.colostate.edu/computationalstatistics/There seems to be an agreement between textbook writers that computational statistics isstatistics that uses computation, often a lot of computation, while statistical computing iscomputational mathematics for statisticians. Both fields are hybrids, but it seems that incomputational statistics the emphasis is on the statistics and in statistical computation theemphasis is on the tools. Of course, not everybody rigorously uses the distinction, and oftenit is quite difficult to draw the line.Initially, most textbooks were in statistical computing (Chambers 1977; Kennedy and Gentle1980), but starting with the influential work of Thisted (1988) (which was published afterthe desktop revolution) we see a shift towards computational statistics. Of the more recenttextbooks, Gentle (2002) is computational statistics, while Gentle (1998a,b) are statisticalcomputation. Gentle is working on another book covering optimization, clearly also in statis-tical computing. Lange (1999) on numerical analysis and Lange (2004) on optimization aresolidly in statistical computation. The recent Marin and Robert (2007) is definitely compu-tational statistics.Statistical computation includes general numerical analysis (floating point, rounding error),numerical linear algebra, optimization, approximation, integration, and Monte Carlo methods.There is usually very little, if anything, on differential equations, partial or otherwise. Thismakes the field quite different from, say, applied mathematics.The book we are reviewing here is partly in statistical computation and partly in computa-tional statistics. For statistical computation it has chapters on continuous (Chapter 2) anddiscrete (Chapter 3) optimization, on numerical integration (Chapter 5), on simulation andMonte Carlo integration (Chapter 6), and on Markov chain Monte Carlo (Chapters 7 and8). In addition, there are computational statistics chapters on EM optimization methods(Chapter 4), on bootstrapping (Chapter 9), on nonparametric density estimation (Chapter10 ) and on bivariate and multivariate smoothing (Chapters 11 and 12).Is it a problem that the two fields are freely mixed? Only in rare cases, I think. One possibleproblem is that numerical linear algebra and error analysis for floating point computation2 Computational Statisticsare missing. That is an unfortunate omission, I think. The authors try to justify this in thepreface by saying they want to concentrate on the big picture, but I think textbooks cannotafford to sweep too much of the nitty-gritty under the rug. You can leave it out of the lectures,but it should be in the textbook.Another possible consequence of not distinguishing the statistical and computational aspectsof the problem is the chapter on the EM algorithm. It takes the likelihood as its startingpoint and immediately embeds the algorithm in a maximum likelihood framework. That maybe historically accurate, but we see from Lange (2004) that it is much clearer to separatethe computational core of the algorithm from its statistical applications. The same thing istrue, I think, for the Bootstrap, which can be quite naturally presented as a numerical orMonte Carlo method to evaluate derivatives. The authors do a pretty good job separatingMCMC from Bayesian inference, but in other chapters the computational techniques and thestatistical applications are pretty tightly intertwined.Sine this is a Journal of Statistical Software review, we should say something about software.It is missing. In the preface, the authors have some obligatory references to S-PLUS, R, andMATLAB, but they take the point of view that “good students can learn as they go”. Thisis undoubtedly true, but rigorous application of this point of view makes it unnecessary towrite textbooks as well. It seems that the authors have realized this as well, since the websiteof the book (which is in its fourth printing) now has code and examples in R. Not in S-PLUSand MATLAB, to be sure.The discussion of the various techniques, both of the computational and statistical aspects,is competent and clear. The accepted wisdom is presented, there are very few idiosyncrasies.So we can characterize this as a solid book, perhaps even as a good book, even though somethings are missing and even though some topics would benefit from a clearer separation ofthe computation and the statistics. I would have no hesitation recommending it to workingstatisticians and quantitative empirical scientists. I would have just a little bit more hesitationusing it in graduate courses. It’s pretty expensive.ReferencesChambers JM (1977). Computational Methods for Data Analysis. Wiley.Gentle JE (1998a). Numerical Linear Algebra for Applications in Statistics. Springer-Verlag.Gentle JE (1998b). Random Number Gneeration and Monte Carlo Methods. Springer-Verlag.Gentle JE (2002). Eelements of Computational Statistics. Springer-Verlag.Kennedy WJ, Gentle JE (1980). Statistical Computing. Marcel Dekker.Lange K (1999). Numerical Analysis for Statisticians. Springer-Verlag.Lange K (2004). Optimization. Springer-Verlag.Marin JM, Robert CP (2007). Bayesian Core: A Practical Approach to ComputationalBayesian Statistics. Springer-Verlag.Thisted RA (1988). Elements of Statistical Computing. Chapman & Hall.Journal of Statistical Software – Book Reviews 3Reviewer:Jan de LeeuwDepartment of StatisticsUniversity of California at Los AngelesLos Angeles, CA 90095-1554, United States of AmericaE-mail: deleeuw@stat.ucla.eduURL: http://www.cuddyvalley.org/Journal of Statistical Software http://www.jstatsoft.org/published by the American Statistical Association http://www.amstat.org/Volume 19, Book Review 1 Published: 2007-03-23March 2007

Computational Statistics

https://www.jstatsoft.org/index.php/jss/article/view/v019b01/152

Computational Statistics

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