In All Likelihood: Statistical Modelling and Inference Using Likelihood - Tapa dura

This is a splendid book with its contents thoroughly covering all likelihood ... Statements are firm, and explanations are full and clear. This book may be used as a reference work. It is strongly recommended as an academic library volume, and individually for statistics lecturers, advanced students, and researchers. (The Mathematical Gazette)

To those of us to whom it is a continuing irritation to be told that there are only two kinds of statisticians, freqentist and Bayesian, this book will come as an enormous relief ... a remarkable book, which deserves the widest distribution; I hope it will gain many converts to the likelihood school. (Biometrics)

Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling.

The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.