Book description
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques.
This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples.
This edition:
Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS.
Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC).
Provides extensive examples throughout the book to complement the theory presented.
Accompanied by a supporting website featuring new material and solutions.
More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students.
Table of contents
 Cover
 Title Page
 Copyright
 Dedication
 Preface
 Preface to the First Edition
 Chapter 1: Preliminaries

Chapter 2: Bayesian inference for the normal distribution
 2.1 Nature of Bayesian inference
 2.2 Normal prior and likelihood
 2.3 Several normal observations with a normal prior
 2.4 Dominant likelihoods
 2.5 Locally uniform priors
 2.6 Highest density regions
 2.7 Normal variance
 2.8 HDRs for the normal variance
 2.9 The role of sufficiency
 2.10 Conjugate prior distributions
 2.11 The exponential family
 2.12 Normal mean and variance both unknown
 2.13 Conjugate joint prior for the normal distribution
 2.14 Exercises on Chapter 2

Chapter 3: Some other common distributions
 3.1 The binomial distribution
 3.2 Reference prior for the binomial likelihood
 3.3 Jeffreys’ rule
 3.4 The Poisson distribution
 3.5 The uniform distribution
 3.6 Reference prior for the uniform distribution
 3.7 The tramcar problem
 3.8 The first digit problem; invariant priors
 3.9 The circular normal distribution
 3.10 Approximations based on the likelihood
 3.11 Reference posterior distributions
 3.12 Exercises on Chapter 3
 Chapter 4: Hypothesis testing

Chapter 5: Twosample problems
 5.1 Twosample problems – both variances unknown
 5.2 Variances unknown but equal
 5.3 Variances unknown and unequal (Behrens–Fisher problem)
 5.4 The Behrens–Fisher controversy
 5.5 Inferences concerning a variance ratio
 5.6 Comparison of two proportions; the $2\times 2$ table
 5.7 Exercises on Chapter 5

Chapter 6: Correlation, regression and the analysis of variance
 6.1 Theory of the correlation coefficient
 6.2 Examples on the use of the correlation coefficient
 6.3 Regression and the bivariate normal model
 6.4 Conjugate prior for the bivariate regression model
 6.5 Comparison of several means – the one way model
 6.6 The two way layout
 6.7 The general linear model
 6.8 Exercises on Chapter 6
 Chapter 7: Other topics
 Chapter 8: Hierarchical models
 Chapter 9: The Gibbs sampler and other numerical methods
 Chapter 10: Some approximate methods

Appendix A: Common statistical distributions
 A.1 Normal distribution
 A.2 Chisquared distribution
 A.3 Normal approximation to chisquared
 A.4 Gamma distribution
 A.5 Inverse chisquared distribution
 A.6 Inverse chi distribution
 A.7 Log chisquared distribution
 A.8 Student’s t distribution
 A.9 Normal/chisquared distribution
 A.10 Beta distribution
 A.11 Binomial distribution
 A.12 Poisson distribution
 A.13 Negative binomial distribution
 A.14 Hypergeometric distribution
 A.15 Uniform distribution
 A.16 Pareto distribution
 A.17 Circular normal distribution
 A.18 Behrens’ distribution
 A.19 Snedecor’s F distribution
 A.20 Fisher’s z distribution
 A.21 Cauchy distribution
 A.22 The probability that one beta variable is greater than another
 A.23 Bivariate normal distribution
 A.24 Multivariate normal distribution
 A.25 Distribution of the correlation coefficient
 Appendix B: Tables
 Appendix C: R programs
 Appendix D: Further reading
 References
 Index
Product information
 Title: Bayesian Statistics: An Introduction, 4th Edition
 Author(s):
 Release date: September 2012
 Publisher(s): Wiley
 ISBN: 9781118332573
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