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Computational Bayesian Statistics An Introduction 1st Edition by Antónia Amaral Turkman, Carlos Daniel Paulino, Peter Müller ISBN 1108481035 9781108481038

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ISBN 10:  1108481035
ISBN 13: 978-1108481038
Author:   M. Antónia Amaral Turkman, Carlos Daniel Paulino, Peter Müller

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software – R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX – makes it useful also for researchers and graduate students from beyond statistics.
 
 

Computational Bayesian Statistics An Introduction 1st Table of contents:

1 Bayesian Inference

1.1 The Classical Paradigm

1.2 The Bayesian Paradigm

1.3 Bayesian Inference

1.3.1 Parametric Inference

1.3.2 Predictive Inference

1.4 Conclusion

2 Representation of Prior Information

2.1 Non-Informative Priors

2.2 Natural Conjugate Priors

3 Bayesian Inference in Basic Problems

3.1 The Binomial [bigwedge] Beta Model

3.2 The Poisson [bigwedge] Gamma Model

3.3 Normal (Known [mu]) [bigwedge] Inverse Gamma Model

3.4 Normal (Unknown [mu, sigma[sup(2)]]) [bigwedge] Je reys’ Prior

3.5 Two Independent Normal Models [bigwedge] Marginal Je reys’ Priors

3.6 Two Independent Binomials [bigwedge] Beta Distributions

3.7 Multinomial [bigwedge] Dirichlet Model

3.8 Inference in Finite Populations

4 Inference by Monte Carlo Methods

4.1 Simple Monte Carlo

4.1.1 Posterior Probabilities

4.1.2 Credible Intervals

4.1.3 Marginal Posterior Distributions

4.1.4 Predictive Summaries

4.2 Monte Carlo with Importance Sampling

4.2.1 Credible Intervals

4.2.2 Bayes Factors

4.2.3 Marginal Posterior Densities

4.3 Sequential Monte Carlo

4.3.1 Dynamic State Space Models

4.3.2 Particle Filter

4.3.3 Adapted Particle Filter

4.3.4 Parameter Learning

5 Model Assessment

5.1 Model Criticism and Adequacy

5.2 Model Selection and Comparison

5.2.1 Measures of Predictive Performance

5.2.2 Selection by Posterior Predictive Performance

5.2.3 Model Selection Using Bayes Factors

5.3 Further Notes on Simulation in Model Assessment

5.3.1 Evaluating Posterior Predictive Distributions

5.3.2 Prior Predictive Density Estimation

5.3.3 Sampling from Predictive Distributions

6 Markov Chain Monte Carlo Methods

6.1 Definitions and Basic Results for Markov Chains

6.2 Metropolis–Hastings Algorithm

6.3 Gibbs Sampler

6.4 Slice Sampler

6.5 Hamiltonian Monte Carlo

6.5.1 Hamiltonian Dynamics

6.5.2 Hamiltonian Monte Carlo Transition Probabilities

6.6 Implementation Details

7 Model Selection and Trans-dimensional MCMC

7.1 MC Simulation over the Parameter Space

7.2 MC Simulation over the Model Space

7.3 MC Simulation over Model and Parameter Space

7.4 Reversible Jump MCMC

8 Methods Based on Analytic Approximations

8.1 Analytical Methods

8.1.1 Multivariate Normal Posterior Approximation

8.1.2 The Classical Laplace Method

8.2 Latent Gaussian Models (LGM)

8.3 Integrated Nested Laplace Approximation

8.4 Variational Bayesian Inference

8.4.1 Posterior Approximation

8.4.2 Coordinate Ascent Algorithm

8.4.3 Automatic Differentiation Variational Inference

9 Software

9.1 Application Example

9.2 The BUGS Project:WinBUGS and OpenBUGS

9.2.1 Application Example: Using R2OpenBUGS

9.3 JAGS

9.3.1 Application Example: Using R2jags

9.4 Stan

9.4.1 Application Example: Using RStan

9.5 BayesX

9.5.1 Application Example: Using R2BayesX

9.6 Convergence Diagnostics: the Programs CODA and BOA

9.6.1 Convergence Diagnostics

9.6.2 The CODA and BOA Packages

9.6.3 Application Example: CODA and BOA

9.7 R-INLA and the Application Example

9.7.1 Application Example

 

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