Computational Bayesian Statistics -- An Introduction

Maria Antonia AMARAL TURKMAN, Carlos Daniel PAULINO and Peter MUELLER

This material will be published by Cambridge University Press as:
Computational Bayesian Statistics -- An Introduction , by M.A. Amaral Turkman, C.D. Paulino, and P. Mueller.

IMS and ISBA members can purchase the book with a significant discount (around $25, I believe).

Table of Contents

1    Bayesian Inference
1.1  The classical paradigm
1.2  The Bayesian paradigm
1.3  Bayesian inference
1.4  Conclusion


2    Representation of Prior Information
2.1  Non-informative priors
2.2  Natural conjugate priors


3    Bayesian Inference in Basic 			     
3.1  The binomial and beta model				     
3.2  The Poisson and gamma model				     
3.3  Normal (known mu)  and  inverse gamma model			     
3.4  Normal (unknown mu, sigma)  and  Jeffreys' prior		     
3.5  Two independent normal models  and  marginal Jeffreys' priors    
3.6  Two independent binomials  and  beta distributions		     
3.7  Multinomial  and  Dirichlet model				     
3.8  Inference in finite populations				     
                                                          

4    Inference by Monte Carlo Methods
4.1  Simple Monte Carlo
4.2  Monte Carlo with importance sampling
4.3  Sequential Monte Carlo


5    Model Assessment	      
5.1  Model criticism and adequacy  
5.2  Model selection and comparison
5.3  Further notes on simulation in model assessment


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                            
6.6  Implementation deta


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
8.2  Latent Gaussian models (LGM)			  
8.3  Integrated nested Laplace approximation (INLA)	  
8.4  Variational Bayesian inference                    


9    Software			      
9.1  Application example		      
9.2  The BUGS project: WinBUGS and OpenBUGS
9.3  JAGS
9.4  Stan
9.5  BayesX
9.6  Convergence diagnostics: the programs CODA and BOA
9.7  R-INLA and the application example

Data files for selected examples:

Errata