Applied statistical inference : likelihood and bayes / Leonhard Held and Daniel Sabanes Bove.

Includes bibliographical references and index.

1. Introduction. -
2. Likelihood. -
3. Elements of Frequentist Inference. -
4. Frequentist Properties of the Likelihood. -
5. Likelihood Inference in Multiparameter Models. -
6. Bayesian Inference. -
7. Model Selection. -
8. Numerical Methods for Bayesian Inference. -
9. Prediction. -
Appendix A. Probabilities, Random Variables and Distributions. -
Appendix B. Some Results from Matrix Algebra and Calculus. - Appendix C. Some Numerical Techniques.-
Notation.-
References.-
Index.

This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.