Bayesian Statistics An Introduction

ISBN-10: 1118332571
ISBN-13: 9781118332573
Edition: 4th 2012
Authors: Peter M. Lee
List price: $63.95 Buy it from $34.93
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Description: The popular & acclaimed Bayesian Statistics: An Introduction, based on the author’s third-year course on Bayesian statistics taught at the University of York, now reaches its fourth edition. It provides a concise account of the way in which the  More...

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Book details

List price: $63.95
Edition: 4th
Copyright year: 2012
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/4/2012
Binding: Paperback
Pages: 486
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 0.968
Language: English

The popular & acclaimed Bayesian Statistics: An Introduction, based on the author’s third-year course on Bayesian statistics taught at the University of York, now reaches its fourth edition. It provides a concise account of the way in which the Bayesian approach to statistics develops and the contrast between it and 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 fourth edition includes significant new material on recent techniques such as variational methods, importance sampling, approximate computation and reversible jump MCMC. All chapters are updated, and the chapter on the Gibbs sampler is heavily expanded.

Preface
Preface to the First Edition
Preliminaries
Probability and Bayes' Theorem
Examples on Bayes' Theorem
Random variables
Several random variables
Means and variances
Exercises on Chapter
Bayesian inference for the normal distribution
Nature of Bayesian inference
Several normal observations with a normal prior
Dominant likelihoods
Locally uniform priors
Highest density regions
Normal variance
HDRs for the normal variance
The role of sufficiency
Conjugate prior distributions
The exponential family
Normal mean and variance both unknown
Conjugate joint prior for the normal distribution
Exercises on Chapter
Some other common distributions
The binomial distribution
Reference prior for the binomial likelihood
Jeffreys' rule
The Poisson distribution
The uniform distribution
Reference prior for the uniform distribution
The tramcar problem
The first digit problem; invariant priors
The circular normal distribution
Approximations based on the likelihood
Reference posterior distributions
Exercises on Chapter
Hypothesis testing
Hypothesis testing
One-sided hypothesis tests
Lindley's method
Point (or sharp) null hypotheses with prior information
Point null hypotheses for the normal distribution
The Doogian philosophy
Exercises on Chapter
Two-sample problems
Two-sample problems - both variances unknown
Variances unknown but equal
Variances unknown and unequal (Behrens-Fisher problem)
The Behrens-Fisher controversy
Inferences concerning a variance ratio
Comparison of two proportions; the 2 � 2 table
Exercises on Chapter
Correlation, regression and the analysis of variance
Theory of the correlation coefficient
Examples on the use of the correlation coefficient
Regression and the bivariate normal model
Conjugate prior for the bivariate regression model
Comparison of several means - the one way model
The two way layout
The general linear model
Exercises on Chapter
Other topics
The likelihood principle
The stopping rule principle
Informative stopping rules
The likelihood principle and reference priors
Bayesian decision theory
Bayes linear methods
Decision theory and hypothesis testing
Empirical Bayes methods
Exercises on Chapter
Hierarchical models
The idea of a hierarchical model
The hierarchical normal model
The baseball example
The Stein estimator
Bayesian analysis for an unknown overall mean
The general linear model revisited
Exercises on Chapter
The Gibbs sampler and other numerical methods
Introduction to numerical methods
The EM algorithm
Data augmentation by Monte Carlo
The Gibbs sampler
Rejection sampling
The Metropolis-Hastings algorithm
Introduction to WinBUGS and OpenBUGS
Generalized linear models
Exercises on Chapter
Some approximate methods
Bayesian importance sampling
Variational Bayesian methods: simple case
Variational Bayesian methods: general case
ABC : Approximate Bayesian Computation
Reversible Jump Markov Chain Monte Carlo
Exercises on Chapter
common statistical distributions
Normal distribution
Chi-squared distribution
Normal approximation to chi-squared
Gamma distribution
Inverse chi-squared distribution
Inverse chi distribution
Log chi-squared distribution
Student's t distribution
Normal/chi-squared distribution
Beta distribution
Binomial distribution
Poisson distribution
Negative binomial distribution
Hypergeometric distribution
Uniform distribution
Pareto distribution
Circular normal distribution
Behrens' distribution
Snedecor's F distribution
Fisher's z distribution
Cauchy distribution
The probability that one beta variable is greater than another
Bivariate normal distribution
Multivariate normal distribution
Distribution of the correlation coefficient
tables
Percentage points of the Behrens-Fisher distribution
Highest density regions for the chi-squared distribution
HDRs for the inverse chi-squared distribution
Chi-squared corresponding to HDRs for log chi-squared
Values of F corresponding to HDRs for log F
R programs
further reading
Robustness
Nonparametric methods
Multivariate estimation
Time series and forecasting
Sequential methods
Numerical methods
Bayesian Networks
General reading
References
Index

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