This book is a contemporary introduction to theory, methods and computation in Bayesian Analysis. It focuses on topics that have stood the test of time and emerging areas such as reference priors, objective Bayes testing, Bayesian model selection and wavelets. No other such book is available in the market.

Klappentext

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing.

Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques.

Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping.

The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

Inhalt

Statistical Preliminaries.- Bayesian Inference and Decision Theory.- Utility, Prior, and Bayesian Robustness.- Large Sample Methods.- Choice of Priors for Low-dimensional Parameters.- Hypothesis Testing and Model Selection.- Bayesian Computations.- Some Common Problems in Inference.- High-dimensional Problems.- Some Applications.