The BUGS Book: A Practical Introduction to Bayesian Analysis

Introduction: Probability and Parameters
Probability
Probability distributions
Calculating properties of probability distributions
Monte Carlo integration

Monte Carlo Simulations Using BUGS
Introduction to BUGS
DoodleBUGS
Using BUGS to simulate from distributions
Transformations of random variables
Complex calculations using Monte Carlo
Multivariate Monte Carlo analysis
Predictions with unknown parameters

Introduction to Bayesian Inference
Bayesian learning
Posterior predictive distributions
Conjugate Bayesian inference
Inference about a discrete parameter
Combinations of conjugate analyses
Bayesian and classical methods

Introduction to Markov Chain Monte Carlo Methods
Bayesian computation
Initial values
Convergence
Efficiency and accuracy
Beyond MCMC

Prior Distributions
Different purposes of priors
Vague, ‘objective’ and ‘reference’ priors
Representation of informative priors
Mixture of prior distributions
Sensitivity analysis

Regression Models
Linear regression with normal errors
Linear regression with non-normal errors
Nonlinear regression with normal errors
Multivariate responses
Generalised linear regression models
Inference on functions of parameters
Further reading

Categorical Data
2 × 2 tables
Multinomial models
Ordinal regression
Further reading

Model Checking and Comparison
Introduction
Deviance
Residuals
Predictive checks and Bayesian p-values
Model assessment by embedding in larger models
Model comparison using deviances
Bayes factors
Model uncertainty
Discussion on model comparison
Prior-data conflict

Issues in Modelling
Missing data
Prediction
Measurement error
Cutting feedback
New distributions
Censored, truncated and grouped observations
Constrained parameters
Bootstrapping
Ranking

Hierarchical Models
Exchangeability
Priors
Hierarchical regression models
Hierarchical models for variances
Redundant parameterisations
More general formulations
Checking of hierarchical models
Comparison of hierarchical models
Further resources

Specialised Models
Time-to-event data
Time series models
Spatial models
Evidence synthesis
Differential equation and pharmacokinetic models
Finite mixture and latent class models
Piecewise parametric models
Bayesian nonparametric models

Different Implementations of BUGS
Introduction BUGS engines and interfaces
Expert systems and MCMC methods
Classic BUGS
WinBUGS
OpenBUGS
JAGS

A Appendix: BUGS Language Syntax
Introduction
Distributions
Deterministic functions
Repetition
Multivariate quantities
Indexing
Data transformations
Commenting

B Appendix: Functions in BUGS
Standard functions
Trigonometric functions
Matrix algebra
Distribution utilities and model checking
Functionals and differential equations
Miscellaneous

C Appendix: Distributions in BUGS
Continuous univariate, unrestricted range
Continuous univariate, restricted to be positive
Continuous univariate, restricted to a finite interval
Continuous multivariate distributions
Discrete univariate distributions
Discrete multivariate distributions

Bibliography

Index