Bayesian Statistics: An Introduction, 4th Edition

Contents

Cover

Title Page

Copyright

Dedication

Preface

Preface to the First Edition

Chapter 1: Preliminaries

1.1 Probability and Bayes’ Theorem

1.2 Examples on Bayes’ Theorem

1.3 Random variables

1.4 Several random variables

1.5 Means and variances

1.6 Exercises on Chapter 1

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

4.1 Hypothesis testing

4.2 One-sided hypothesis tests

4.3 Lindley’s method

4.4 Point (or sharp) null hypotheses ...