An Introduction to Bayesian Analysis: Theory and Methods / Edition 1

An Introduction to Bayesian Analysis: Theory and Methods / Edition 1

by Jayanta K. Ghosh, Mohan Delampady, Tapas Samanta
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9781441923035
Publisher:
Springer New York
Publication date:
11/19/2010
Series:
Springer Texts in Statistics Series, #147
Edition description:
Softcover reprint of hardcover 1st ed. 2006
Pages:
354
Product dimensions:
6.10(w) x 9.00(h) x 0.90(d)

Related Subjects

Table of Contents

1Statistical preliminaries1
2Bayesian inference and decision theory29
3Utility, prior, and Bayesian robustness65
4Large sample methods99
5Choice of priors for low-dimensional parameters121
6Hypothesis testing and model selection159
7Bayesian computations205
8Some common problems in inference239
9High-dimensional problems255
10Some applications289
ACommon statistical densities303
BBirnbaum's theorem on likelihood principle307
CCoherence311
DMicroarray313
EBayes sufficiency315

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