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Texts in Statistical Science
Baesian
Data Analysis
SECOND EDITION
Contents
List of models
List of examples
Preface
Part 1: Fudamentals of Bayesian Inference
1 Background
1.1 Overview
1.2 General notation for statistical inference
1.3 Bayesia inference
1.4 Example: inference about a genetic probability
1.5 Probability as a measure of uncertainty
1.6 Example of probability assignment: football point spreads
1.7 Example of probability assignment: estimating the accuracy
of record linkage
1.8 Some useful results frm probability theory
1.9 Summarizing inferences by simulation
1.10 Computation and software
1.11 Bibliographic note
1.12 Exercises
2 Single-parameter models
2.1 Estimating a probability from binomial data
2.2 Posterior distribution as compromise between data and prior
information
2.3 Summarizing posterior inference
2.4 Informative prior distributions
2.5 Example: estimating the probability of a female birth given
placenta previa
2.6 Estimating the mean of a normal distribution with known
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variance 46
2.7 Other standard single-parameter models 49
2.8 Example: informative prior distribution and multilevel struc-
ture for estimating cancer rates 55
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CONTENTS
2.9 Noninformative prior distributions 61
2.10 Bibliographic note 65
2.11 Exercises 67
3 Introduction to multiparameter models 73
3.1 Averaging over 'nuisance parameters' 73
3.2 Normal data with a noninformative prior distribution 74
3.3 Normal data with a conjugate prior distribution 78
3.4 Normal data with a semi-conjugate prior distribution 80
3.5 The multinomial model 83
3.6 The multivariate normal model 85
3.7 Example: anlysis of a bioassay experiment 88
3.8 Summary of elementary modeling and computation 93
3.9 Bibliographic note 94
3.10 Exercises 95
4 Large-sample inference and frequency properties of Bayesian
inference 101
4.1 Normal approximations to the posterior distribution 101
4.2 Large-sample theory 106
4.3 Counterexamples to the theorems 108
4.4 Frequency evaluations of Bayesian inferences 111
4.5 Bibliographic note 113
4.6 Exercises 113
Part II: Fudamentals of Bayesian Data Analysis 115
5 Hierarchical models 117
5.1 Constructing a parameterized prior distribution 118
5.2 Exchangeability and setting up hierarchical models 121
5.3 Computation with hierarchical models 125
5.4 Estimating an exchangeable set of parameters from a normal
model 131
5.5 Example: combining information from educational testing
experiments in eight schools 138
5.6 Hierarchical modeling applied to a meta-analysis 145
5.7 Bibliographic note 150
5.8 Exercises 152
6 Model checking and improvement 157
6.1 The place of model checking in applied Bayesian statistics 157
6.2 Do the inferences from the model make sense? 158
6.3 Is the model consistent with data? Posterior predictive
checking 159
6.4 Graphical posterior predictive checks
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