An Introduction to Bayesian Analysis

Theory and Methods

  • Jayanta K. Ghosh
  • Mohan Delampady
  • Tapas Samanta

Part of the Springer Texts in Statistics book series (STS)

Table of contents

About this book

Introduction

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.

J.K. Ghosh has been Director and Jawaharlal Nehru Professor at the Indian Statistical Institute and President of the International Statistical Institute. He is currently a professor of statistics at Purdue University and professor emeritus at the Indian Statistical Institute. He has been the editor of Sankhya and has served on the editorial boards of several journals including the Annals of Statistics. His current interests in Bayesian analysis include asymptotics, nonparametric methods, high-dimensional model selection, reliability and survival analysis, bioinformatics, astrostatistics and sparse and not so sparse mixtures.

Mohan Delampady and Tapas Samanta are both professors of statistics at the Indian Statistical Institute and both are interested in Bayesian inference, specifically in topics such as model selection, asymptotics, robustness and nonparametrics.

Keywords

statistical computing statistical inference statistics

Authors and affiliations

  • Jayanta K. Ghosh
    • 1
    • 2
  • Mohan Delampady
    • 3
  • Tapas Samanta
    • 2
  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Indian Statistical InstituteKolkataIndia
  3. 3.Indian Statistical InstituteBangaloreIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-35433-0
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-40084-6
  • Online ISBN 978-0-387-35433-0
  • Series Print ISSN 1431-875X
  • About this book