An Introduction to Bayesian Analysis: Theory and Methods

✍ Scribed by Jayanta K. Ghosh, Mohan Delampady, Tapas Samanta

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 355
• Series: Springer Texts in Statistics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Advisors
......Page 1
Springer texts in statistics
......Page 2
Title
......Page 3
Copyright
......Page 4
Preface
......Page 6
Contents
......Page 8
1. Statistical preliminaries
......Page 13
2. Bayesian inference and decision theory
......Page 40
3. Utility, prior, and Bayesian robustness
......Page 75
4. Large sample methods
......Page 108
5. Choice of priors for low-dimensional parameters
......Page 129
6. Hypothesis testing and model selection
......Page 166
7. Bayesian computations
......Page 212
8. Some common problems in inference
......Page 245
9. High-dimensional problems
......Page 261
10. Some applications
......Page 295
A. Common statistical densities
......Page 309
B. Birnbaum's theorem on likelihood principle
......Page 313
C. Coherence
......Page 316
D. Microarray
......Page 318
E. Bayes sufficiency
......Page 320
References
......Page 321
Author index
......Page 342
Subject index
......Page 347
Springer texts in statistics (cont.)
......Page 355