Introduction to Matrix Analytic Methods in Stochastic Modeling

chapter deals with regression analysis; the sections are “ Introduction,” ‘The Data,” “Background,” “The Gauge” (which includes a physical model), “Investigations,” “Theory (The Simple Linear Model, Model Mis t, Transformations, Residual Plots, Replicate Measurements, Con dence and Prediction Bands, Calibration, Maximum Likelihood, An Alternative),” “Exercises,” “Notes,” and “References. ” I liked this book—its organization, its presentation, and the style of writing. In my scanning, I did not catch any typographical errors. The work clearly gives the impression that these authors have taken the time to think through what they wanted to do and have made an effort to do it. The headings of the chapters listed previously indicate the depth of their coverage; I would like to highlight the contents of Appendix A, titled “Writing Lab Reports. ” Everyone agrees how important developing writing and communication skills are. Here one can  nd step-by-step instructions on such topics as organization, grammar (including examples of grammatical problems), clarity and structure of prose, and revising and proofreading. Quite frankly, I cannot think of any statistics book, particularly at this level and for this type of material, in which such discussions can be found. This appendix, even by itself, should be on the must-read list for all students, including graduate students. Of course, there are additional topics that one would like to see included. Some of these are even mentioned in the article titled “Teaching Statistics Theory Through Applicaitons,” (Nolan and Speed 1999, pp. 370–375) by the same authors. The additional topics could include more details on things like the moment-generating function, the methods of deriving distributions of transformation of random variables, concepts of estimation such as suf ciency and minimum variance, and others. In fact, the authors might consider doing a second volume; that way more time and space can be devoted to more concepts. More guidelines on how to use a particular computer package (the authors mention two) in a given situation would be helpful; this could include step-by-step instructions and annotated printouts. I also think (the title of the book suggests this) that, given the nature of the material, this way of teaching would require (and greatly bene t from) a solid support mechanism from outside the classroom. An essential component of such support would have to be recitation and/or lab sections (as the authors have used) with dependable teaching assistants. It seems fair to say that the look and feel of many popular mathematical statistics books have not changed much in years. The standard formula is to do much theory  rst and then some examples; many of these examples often appear as afterthoughts. Recently however, there have been calls for a change in this formula (e.g., see Cobb and Moore 1997). One suggestion is to shift the focus to problem solving, using existing (or developing new) mathematical-statistical and subject-matter theory rather than developing new theory to solve problems that could arise in the future. An implementation of this strategy would require a paradigm shift in the teaching of mathematical statistics, and that is easier said than done. However, it is worth pointing out that a similar paradigm shift did take place in the teaching of statistical methods a few years ago. As I recall, following discussions between academia and industry, textbooks began to appear that emphasized the problem-solving approach to learning statistics by providing more real-life examples and case studies. Thanks to these authors, there are a number of  ne books and supplementary materials available now for teaching statistical methods, particularly at the undergraduate level. The present book could start a similar trend among the mathematical statistics textbooks.