Contents
Abstract ....................................................................ix
Acknowledgements ...........................................................xi
Preface ....................................................................xiii
Overview .................................................................. xv
Chapter 1: Bayesian Basics Part 1 ...............................................1
1.1 Introduction ........................................................1
1.2 Bayes’ rule ..........................................................2
1.3 Bayes factors ........................................................9
1.4 Bayesian models ....................................................11
1.5 The posterior distribution ............................................ 12
1.6 The proportionality formula ..........................................13
1.7 Continuous parameters .............................................19
1.8 Finite and innite population inference .................................22
1.9 Continuous data ...................................................23
1.10 Conjugacy .........................................................24
1.11 Bayesian point estimation ............................................25
1.12 Bayesian interval estimation ..........................................26
1.13 Inference on functions of the model parameter .........................31
1.14 Credibility estimates ................................................34
Chapter 2: Bayesian Basics Part 2 ..............................................61
2.1 Frequentist characteristics of Bayesian estimators ........................61
2.2 Mixture prior distributions ...........................................74
2.3 Dealing with a priori ignorance .......................................80
2.4 The Jeffreys prior ...................................................81
2.5 Bayesian decision theory .............................................86
2.6 The posterior expected loss .........................................93
2.7 The Bayes estimate .................................................98
Chapter 3: Bayesian Basics Part 3 .............................................109
3.1 Inference given functions of the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.2 Bayesian predictive inference ........................................116
3.3 Posterior predictive p-values ........................................130
3.4 Bayesian models with multiple parameters ............................135
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