Analyzing Medical Data Using S-PLUS

With its breadth of coverage, this book would make a wonderful reference source for any statistician’s bookshelf. It reminds me a bit of an encyclopedia, in that many topics are covered, and each is presented with a short description and illustrative example. The methods appear in the context of related approaches, and the plentiful references give clear direction for where to go for more detailed information. I highly recommend this book as a resource, the place to go  rst with a new query in search of background and further direction. The  ip side of the encyclopedic approach is that I have some reservations about using this book as a text. Because so many methods are discussed, most get only a brief description and a toy example. Chapter 9, on nonparametric density estimation, is a welcome exception, with detailed discussions of histogram and kernel estimators. Most other methods, especially those in Part I, have the quantity-versus-depth trade-off made in favor of quantity. The fact that nearly all examples are on small, synthetic datasets may make it dif cult for students to see the bigger picture and to have some idea of how to decide which method is most appropriate for a particular problem. It would have been really nice to have some larger case studies used as examples throughout the book. In the Preface, Gentle states that this book arose from a course he teaches (p. viii). However, he also notes (p. xi) that when he teaches it, he includes “more examples, and more extensive examples,” and that additional material is available online through the web page for the book. If this book had truly been meant as a text, it should have included more of these examples. As it stands, it is imperative for the instructor to incorporate more examples, and to ensure that the students get a sense of the big picture. On the plus side, there are exercises at the end of each chapter, with a good balance of theoretical and computational exercises. A number of exercises require implementation of methods, a vital part of learning for students. There are also a number of interesting-looking problems involving simulations, which require students to implement a procedure as well as to observe its behavior, thus learning both how and when to use it. As a further boon for students, Appendix D contains hints for some problems and sketches of solutions for others. Appendix A provides a detailed discussion of Monte Carlo studies, including motivation, design, implementation, and reporting. An example is developed through all of these stages, with an ongoing commentary. This fully developed example clearly illustrates the numerous issues raised in the discussion and is ideal for researchers or students new to the serious use of Monte Carlo experiments. If the other chapters had been developed similarly, this would have made a terri c text. As it is, there is more than enough material for one-semester course. In fact, there is enough material for a two-semester sequence, which gives an instructor a fair amount of  exibility in deciding which parts of the book to emphasize in a class. Because most sections are fairly self-contained, it is quite feasible to cherry-pick one’s favorites in creating a lesson plan. There are a minimal number of typographical errors. No book is perfect, and the proofreading seems generally quite good. I do have a minor complaint about notation. In general, the notation is quite consistent, and Appendix C provides a thorough listing of the notation used in the book. However, as stated in the Preface (p. xiii), Gentle does “not distinguish vectors and scalars in the notation; thus x may represent either a scalar or a vector, and xi may represent either the ith element of an array or the i th vector in a set of vectors. ” Usually it is quite clear from the context what a particular xi means, although there are a couple of situations where the reader would be greatly aided by a more clear distinction. For example, Table 7.1 (p. 172) displays an example dataset with four vector-valued observations of dimension seven, labeling the observations as “1,” “2,” “3,” and “4,” and the variables (elements of the vectors) as x1 through x7 . A discussion of rescaling on p. 173 contains the sentence: “Thus, for x1 in Table 7.1, the values become 1.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0,” which uses x1 in the opposite sense than the table, creating the potential for much confusion. In conclusion, I wish to commend Gentle for his efforts on this well-written book. The vast coverage of methodology makes this book a valuable resource for any statistician involved with computational statistics (just about everyone who uses data), as well as for applied researchers in other  elds who use advanced statistical methods.