Applied Statistical Inference: Likelihood and Bayes

✍ Scribed by Leonhard Held, Daniel Sabanés Bové (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2014
• Tongue: English
• Leaves: 381
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XIII
Introduction....Pages 1-12
Likelihood....Pages 13-50
Elements of Frequentist Inference....Pages 51-78
Frequentist Properties of the Likelihood....Pages 79-122
Likelihood Inference in Multiparameter Models....Pages 123-165
Bayesian Inference....Pages 167-219
Model Selection....Pages 221-245
Numerical Methods for Bayesian Inference....Pages 247-289
Prediction....Pages 291-316
Back Matter....Pages 317-376

✦ Subjects

Statistical Theory and Methods; Statistics for Life Sciences, Medicine, Health Sciences; Statistics and Computing/Statistics Programs