In All Likelihood

Abstract This book presents the role of likelihood in a wide range of statistical problems, from a simple comparison of two accident rates to complex studies requiring generalized linear or semiparametric modelling. The book emphasizes that the likelihood is not simply a device to produce an estimate, but more importantly it provides a rich framework for modelling. Although it relies on mathematical results, the book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With currently available computing power, examples are not contrived to allow a closed analytical solution, and the book concentrates 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, hierarchical generalized linear models, nonparametric smoothing, robustness, EM algorithm and empirical likelihood.