This text concentrates on what can be achieved using the likelihood/Fisherian methods of taking into account uncertainty when studying a statistical problem. It takes the concept of the likelihood as the best method for unifying the demands of statistical modeling and theory of inference. Every likelihood concept is illustrated with realistic examples ranging from a simple comparison of two accident rates to complex studies that require generalized linear or semiparametric modeling. The emphasis is on likelihood not as just a device used to produce an estimate, but as an important tool for modeling. 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. This book presents the role of likelihood in a whole range of statistical problems, from a simple comparison of two accident rates to complex studies requiring generalized linear or semiparametric modeling. The book emphasizes that the likelihood is not simply a device to produce an estimate, but more importantly it is a tool for modeling. 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, generalized linear mixed models, nonparametric smoothing, robustness, EM algorithm and empirical likelihood. --back cover 1. Introduction -- 2. Elements Of Likelihood Inference -- 3. More Properties Of The Likelihood -- 4. Basic Models And Simple Applications -- 5. Frequentist Properties -- 6. Modelling Relationships: Regression Models -- 7. Evidence And The Likelihood Principle -- 8. Score Function And Fisher Information -- 9. Large-sample Results -- 10. Dealing With Nuisance Parameters -- 11. Complex Data Structure -- 12. Em Algorithm -- 13. Robustness Of Likelihood Specification -- 14. Estimating Equation And Quasi-likelihood -- 15. Empirical Likelihood -- 16. Likelihood Of Random Parameters -- 17. Random And Mixed Effects Models -- 18. Nonparametric Smoothing. Yudi Pawitan. Includes Bibliographical References (p. [503]-514) And Index. 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 of the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference Statistical modelling and inference have grown, above all else, to deal with variation and uncertainty.
