Elements of Computational Statistics

Rating:
Summary: not just statistical computing
Review: At first I thought this was a revision of his excellent book with Kennedy on statistical computing. But after browsing it I discovered it was a book on a subject that is near and dear to my "computationally intensive statistical methods". I then discovered a whole chapter on bootstrap methods, a topic of have studied, taught and written about!

I concur with the editorial reviewer on the content of the book. So I will not go into a detailed description that would just be repetitious.

The distinction that Gentle chooses to make between statistical computing and computational statistics is interesting. He sees statistical computing as methods of calculation. So statistical computing encompasses numerical analysis methods, Monte Carlo integration etc. On the other hand computational statistics involves computer-intensive methods like bootstrap, jackknife, cross-validation, permutation or randomization tests, projection pursuit, function estimation, data mining, clustering and kernel methods. But Gentle includes some other tools that are not necessarily intensive such as transformations, parametric estimation and some graphical methods.

Where would you put the EM algorithm and Markov Chain Monte Carlo? These are computational algorithms and hence I think belong under statistical computing, but they also can be computationally intensive methods especially MCMC. What does Gentle say. Well Chapter 1 is on preliminaries and he includes a section on the role of optimization in statistical inference. Here the EM algorithm is well placed as well as many other computing techniques like iteratively reweighted least squares, Lagrange multipliers and quasi-Newton methods.

The bootstrap chapter provides a self-contained introduction to the topic supported by a good choice of references. Variance estimation and the various types of bootstrap confidence intervals for parameters are discussed. Independent samples are the main topic though section 4.4 briefly describes dependency cases such as in regression analysis and time series.

The book is up-to-date and authoritative and is a very good choice for anyone interested in computer-intensive methods and its connections to statistical computing. This is the way modern statistics is moving and so is worth looking at.