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Summary: Statistical Modelling and Inference for this Century
Review: I used "In All Likelihood" as a basis for the 13 week 3rd year Mathematical Statistics/ Statistical Inference course I have almost finished teaching. Finding this book at Amazon was my very good fortune. It is exactly the way I would have tried to write such a course but I couldn't have done as good a job as Pawitan. I like this book because it covers all the theory, such as, sufficiency, completeness, minimum variance unbiased estimation, large sample asymptotics etc. But the beauty of the book lies in the relevant, modern examples. Likelihood functions are liberally graphed for the many examples. These are created in R; if you are an R user, or wish to be, you'll like the availability of the source code. If you're not into R, it won't make a difference to the usability of the book. Books like Bickel & Doksum, Casella & Berger and Rice, have the theory, but not the range of practical examples that add so much to "In All Likelihood". Pawitan's theoretical sections are comparatively easy to follow. Pawitan points out important results rather than the reader needing to surmise what bits of theory are useful in practice. On the other hand, since reading Pawitan I can now read sections out of McCullough and Nelder, and other applications books, no longer feeling I have missed some important background theory. I see signs of good teaching practice throughout "In All Likelihood" that make it easy to learn and teach from. For example, difficult concepts are often initially introduced in an example and then reintroduced in technical detail. This way the learner feels some familiarity the second time around. Semester is nearly over. We covered the first nine chapters (out of 18) in 38 hours of lectures. I'm reading the rest of the book now. Every page or two something else I have heard, seen or read in the past begins to make more sense. Examples of topics in the second half of the book are the EM algorithm, Generalized Estimating Equations and random/mixed effects models. I told my students that if they considered buying a book for their future in statistics, "In All Likelihood" is a very good one.
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