Preface
Part I�� Fundamentals of Bayesian Inference
1 Probability and inference
I��I The three steps of Bayesian data analysis
1��2 General notation for statistical inference
1��3 Bayesian inference
1��4 Discrete examples�� genetics and spell checking
1��5 Probability as a measure of uncertainty
1��6 Example�� probabilities from football point spreads
1��7 Example�� calibration for record linkage
1��8 Some useful results from probability theory
1��9 Computation and software
I��I0 Bayesian inference in applied statistics
i��Ii Bibliographic note
1��12 Exercises
2 Single-parameter models
2��1 Estimating a probability from binomial data
2��2 Posterior as compromise between data and prior information
2��3 Summarizing posterior inference
2��4 Informative prior distributions
2��5 Normal distribution with known variance
2��6 Other standard single-parameter models
2��7 Example�� informative prior distribution for cancer rates
2��8 Noninformative prior distributions
2��9 Weakly informative prior distributions
2��10 Bibliographic note
2��11 Exercises
3 Introduction to multiparameter models
3��1 Averaging over 'nuisance parameters'
3��2 Normal data with a noninformative prior distribution
3��3 Normal data with a conjugate prior distribution
3��4 Multinomial model for categorical data
3��5 Multivariate normal model with known variance
3��6 Multivariate normal with unknown mean and variance
3��7 Example�� analysis of a bioassay experiment
3��8 Summary of elementary modeling and computation
3��9 Bibliographic note
3��10 Exercises
4 Asymptotics and connections to non-Bayesian approaches
4��1 Normal approximations to the posterior distribution
4��2 Large-sample theory
4��3 Counterexamples to the theorems
4��4 Frequency evaluations of Bayesian inferences
4��5 Bayesian interpretations of other statistical methods
4��6 Bibliographic note
4��7 Exercises
5 Hierarchical models
5��1 Constructing a parameterized prior distribution
5��2 Exchangeability and hierarchical models
5��3 Bayesian analysis of conjugate hierarchical models
5��4 Normal model with exchangeable parameters
5��5 Example�� parallel experiments in eight schools
5��6 Hierarchical modeling applied to a meta-analysis
5��7 Weakly informative priors for variance parameters
5��8 Bibliographic note
5��9 Exercises

Part II�� Fundamentals of Bayesian Data Analysis
6 Model checking
6��1 The place of model checking in applied Bayesian statistics
6��2 Do the inferences from the model make sense?
6��3 Posterior predictive checking
6��4 Graphical posterior predictive checks
6��5 Model checking for the educational testing example
6��6 Bibliographic note
6��7 Exercises
? Evaluating�� comparing�� and expanding models
7��1 Measures of predictive accuracy
7��2 Information criteria and cross-validation
7��3 Model comparison based on predictive performance
7��4 Model comparison using Bayes factors
7��5 Continuous model expansion
7��6 Implicit assumptions and model expansion�� an example
7��7 Bibliographic note
7��8 Exercises
8 Modeling accounting for data collection
8��1 Bayesian inference requires a model for data collection
8��2 Data-collection models and ignorability
8��3 Sample surveys
8��4 Designed experiments
8��5 Sensitivity and the role of randomization
8��6 Observational studies
8��7 Censoring and truncation
8��8 Discussion
8��9 Bibliographic note
8��10 Exercises
9 Decision analysis
9��1 Bayesian decision theory in different contexts
9��2 Using regression predictions�� survey incentives
9��3 Multistage decision making�� medical screening
9��4 Hierarchical decision analysis for home radon
9��5 Personal vs�� institutional decision analysis
9��6 Bibliographic note
9��7 Exercises

Part III�� Advanced Computation
10 Introduction to Bayesian computation
10��1 Numerical integration
10��2 Distributional approximations
10��3 Direct simulation and rejection sampling
10��4 Importance sampling
10��5 How many simulation draws are needed?
10��6 Computing environments
10��7 Debugging Bayesian computing
10��8 Bibliographic note
10��9 Exercises
11 Basics of Markov chain simulation
11��1 Gibbs sampler
11��2 Metropolis and Metropolis-Hastings algorithms
11��3 Using Gibbs and Metropolis as building blocks
11��4 Inference and assessing convergence
11��5 Effective number of simulation draws
11��6 Example�� hierarchical normal model
11��7 Bibliographic note
11��8 Exercises
12 Computationally efficient Markov chain simulation
12��1 Efficient Gibbs samplers
12��2 Efficient Metropolis jumping rules
12��3 Further extensions to Gibbs and Metropolis
12��4 Hamiltonian Monte Carlo
12��5 Hamiltonian Monte Carlo for a hierarchical model
12��6 Stan�� developing a computing environment
12��7 Bibliographic note
12��8 Exercises
13 Modal and distributional approximations
13��1 Finding posterior modes
13��2 Boundary-avoiding priors for modal summaries
13��3 Normal and related mixture approximations
13��4 Finding marginal posterior modes using EM
13��5 Conditional and marginal posterior approximations
13��6 Example�� hierarchical normal model ��continued��
13��7 Variational inference
13��8 Expectation propagation
13��9 Other approximations
13��10 Unknown normalizing factors
13��11 Bibliographic note
13��12 Exercises

Part IV�� Regression Models
14 Introduction to regression models
14��1 Conditional modeling
14��2 Bayesian analysis of classical regression
14��3 Regression for causal inference�� incumbency and voting
14��4 Goals of regression analysis
14��5 Assembling the matrix of explanatory variables
14��6 Regularization and dimension reduction
14��7 Unequal variances and correlations
14��8 Including numerical prior information
14��9 Bibliographic note
14��10 Exercises
15 Hierarchical linear models
15��1 Regression coefficients exchangeable in batches
15��2 Example�� forecasting U��S�� presidential elections
15��3 Interpreting a normal prior distribution as extra data
15��4 Varying intercepts and slopes
15��5 Computation�� batching and transformation
15��6 Analysis of variance and the batching of coefficients
15��7 Hierarchical models for batches of variance components
15��8 Bibliographic note
15��9 Exercises
16 Generalized linear models
16��1 Standard generalized linear model likelihoods
16��2 Working with generalized linear models
16��3 Weakly informative priors for logistic regression
16��4 Overdispersed Poisson regression for police stops
16��5 State-level opinons from national polls
16��6 Models for multivariate and multinomial responses
16��7 Loglinear models for multivariate discrete data
16��8 Bibliographic note
16��9 Exercises
17 Models for robust inference
17��1 Aspects of robustness
17��2 Overdispersed versions of standard models
17��3 Posterior inference and computation
17��4 Robust inference for the eight schools
17��5 Robust regression using t-distributed errors
17��6 Bibliographic note
17��7 Exercises
18 Models for missing data
18��1 Notation
18��2 Multiple imputation
18��3 Missing data in the multivariate normal and t models
18��4 Example�� multiple imputation for a series of polls
18��5 Missing values with counted data
18��6 Example�� an opinion poll in Slovenia
18��7 Bibliographic note
18��8 Exercises

Part V�� Nonlinear and Nonparametric Models
19 Parametric nonlinear models
19��1 Example�� serial dilution assay
19��2 Example�� population toxicokinetics
19��3 Bibliographic note
19��4 Exercises
20 Basis function models
20��1 Splines and weighted sums of basis functions
20��2 Basis selection and shrinkage of coefficients
20��3 Non-normal models and regression surfaces
20��4 Bibliographic note
20��5 Exercises
21 Gaussian process models
21��1 Gaussian process regression
21��2 Example�� birthdays and birthdates
21��3 Latent Gaussian process models
21��4 Functional data analysis
21��5 Density estimation and regression
21��6 Bibliographic note
21��7 Exercises
22 Finite mixture models
22��1 Setting up and interpreting mixture models
22��2 Example�� reaction times and schizophrenia
22��3 Label switching and posterior computation
22��4 Unspecified number of mixture components
22��5 Mixture models for classification and regression
22��6 Bibliographic note
22��7 Exercises
23 Dirichlet process models
23��1 Bayesian histograms
23��2 Dirichlet process prior distributions
23��3 Dirichlet process mixtures
23��4 Beyond density estimation
23��5 Hierarchical dependence
23��6 Density regression
23��7 Bibliographic note
23��8 Exercises

Appendixes
A Standard probability distributions
A��1 Continuous distributions
A��2 Discrete distributions
A��3 Bibliographic note
B Outline of proofs of limit theorems
B��1 Bibliographic note
C Computation in R and Stan
C��1 Getting started with R and Stan
C��2 Fitting a hierarchical model in Stan
C��3 Direct simulation�� Gibbs�� and Metropolis in R
C��4 Programming Hamiltonian Monte Carlo in R
C��5 Further comments on computation
C��6 Bibliographic note
References
Author Index
Subject Index