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| Preface | |
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| Introduction: Probability and parameters | |
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| Probability | |
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| Probability distributions | |
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| Calculating properties of probability distributions | |
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| Monte Carlo integration | |
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| Monte Carlo simulations using BUGS | |
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| Introduction to BUGS | |
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| Background | |
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| Directed graphical models | |
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| The BUGS language | |
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| Running BUGS models | |
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| Running WinBUGS for a simple example | |
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| DoodleBUGS | |
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| Using BUGS to simulate from distributions | |
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| Transformations of random variables | |
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| Complex calculations using Monte Carlo | |
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| Multivariate Monte Carlo analysis | |
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| Predictions with unknown parameters | |
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| Introduction to Bayesian inference | |
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| Bayesian learning | |
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| Bayes' theorem for observable quantities | |
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| Bayesian inference for parameters | |
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| Posterior predictive distributions | |
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| Conjugate Bayesian inference | |
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| Binomial data | |
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| Normal data with unknown mean, known variance | |
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| Inference about a discrete parameter | |
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| Combinations of conjugate analyses | |
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| Bayesian and classical methods | |
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| Likelihood-based inference | |
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| Exchangeability | |
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| Long-run properties of Bayesian methods | |
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| Model-based vs procedural methods | |
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| The "likelihood principle" | |
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| Introduction to Markov chain Monte Carlo methods | |
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| Bayesian computation | |
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| Single-parameter models | |
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| Multi-parameter models | |
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| Monte Carlo integration for evaluating posterior integrals | |
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| Markov chain Monte Carlo methods | |
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| Gibbs sampling | |
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| Gibbs sampling and directed graphical models | |
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| Derivation of full conditional distributions in BUGS | |
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| Other MCMC methods | |
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| Initial values | |
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| Convergence | |
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| Detecting convergence/stationarity by eye | |
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| Formal detection of convergence/stationarity | |
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| Efficiency and accuracy | |
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| Monte Carlo standard error of the posterior mean | |
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| Accuracy of the whole posterior | |
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| Beyond MCMC | |
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| Prior distributions | |
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| Different purpose of priors | |
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| Vague, "objective," and "reference" priors | |
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| Introduction | |
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| Discrete uniform distributions | |
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| Continuous uniform distributions and Jeffreys prior | |
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| Location parameters | |
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| Proportions | |
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| Counts and rates | |
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| Scale parameters | |
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| Distributions on the positive integers | |
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| More complex situations | |
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| Representation of informative priors | |
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| Elicitation of pure judgement | |
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| Discounting previous data | |
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| Mixture of prior distributions | |
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| Sensitivity analysis | |
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| Regression models | |
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| Linear regression with normal errors | |
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| Linear regression with non-normal errors | |
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| Non-linear regression with normal errors | |
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| Multivariate responses | |
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| Generalised linear regression models | |
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| Inference on functions of parameters | |
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| Further reading | |
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| Categorical data | |
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| 2 X 2 tables | |
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| Tables with one margin fixed | |
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| Case-control studies | |
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| Tables with both margins fixed | |
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| Multinomial models | |
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| Conjugate analysis | |
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| Non-conjugate analysis-parameter constraints | |
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| Categorical data with covariates | |
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| Multinomial and Poisson regression equivalence | |
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| Contingency tables | |
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| Ordinal regression | |
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| Further reading | |
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| Model checking and comparison | |
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| Introduction | |
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| Deviance | |
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| Residuals | |
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| Standardised Pearson residuals | |
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| Multivariate residuals | |
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| Observed p-values for distributional shape | |
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| Deviance residuals and tests of fit | |
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| Predictive checks and Bayesian p-values | |
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| Interpreting discrepancy statistics - how big is big? | |
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| Out-of-sample prediction | |
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| Checking functions based on data alone | |
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| Checking functions based on data and parameters | |
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| Goodness of fit for grouped data | |
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| Model assessment by embedding in larger models | |
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| Model comparison using deviances | |
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| pD: The effective number of parameters | |
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| Issues with pD | |
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| Alternative measures of the effective number of parameters | |
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| DIC for model comparison | |
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| How and why does WinBUGS partition DIC and pD? | |
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| Alternatives to DIC | |
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| Bayes factors | |
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| Lindley-Bartlett paradox in model selection | |
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| Computing marginal likelihoods | |
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| Model uncertainty | |
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| Bayesian model averaging | |
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| MCMC sampling over a space of models | |
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| Model averaging when all models are wrong | |
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| Model expansion | |
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| Discussion on model comparison | |
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| Prior-data conflict | |
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| Identification of prior-data conflict | |
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| Accommodation of prior-data conflict | |
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| Issues in Modelling | |
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| Missing data | |
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| Missing response data | |
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| Missing covariate data | |
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| Prediction | |
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| Measurement error | |
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| Cutting feedback | |
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| New distributions | |
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| Specifying a new sampling distribution | |
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| Specifying a new prior distribution | |
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| Censored, truncated, and grouped observations | |
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| Censored observations | |
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| Truncated sampling distributions | |
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| Grouped, rounded, or interval-censored data | |
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| Constrained parameters | |
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| Univariate fully specified prior distributions | |
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| Multivariate fully specified prior distributions | |
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| Prior distributions with unknown parameters | |
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| Bootstrapping | |
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| Ranking | |
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| Hierarchical models | |
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| Exchangeability | |
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| Priors | |
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| Unit-specific parameters | |
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| Parameter constraints | |
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| Priors for variance components | |
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| Hierarchical regression models | |
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| Data formatting | |
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| Hierarchical models for variances | |
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| Redundant parameterisations | |
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| More general formulations | |
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| Checking of hierarchical models | |
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| Comparison of hierarchical models | |
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| "Focus": The crucial element of model comparison in hierarchical models | |
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| Further resources | |
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| Specialised models | |
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| Time-to-event data | |
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| Parametric survival regression | |
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| Time series models | |
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| Spatial models | |
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| Intrinsic conditionally autoregressive (CAR) models | |
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| Supplying map polygon data to WinBUGS and creating adjacency matrices | |
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| Multivariate CAR models | |
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| Proper CAR model | |
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| Poisson-gamma moving average models | |
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| Geostatistical models | |
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| Evidence synthesis | |
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| Meta-analysis | |
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| Generalised evidence synthesis | |
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| Differential equation and pharmacokinetic models | |
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| Finite mixture and latent class models | |
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| Mixture models using an explicit likelihood | |
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| Piecewise parametric models | |
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| Change-point models | |
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| Splines | |
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| Semiparametric survival models | |
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| Bayesian nonparametric models | |
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| Dirichlet process mixtures | |
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| Stick-breaking implementation | |
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| Different implementations of BUGS | |
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| Introduction-BUGS engines and interfaces | |
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| Expert systems and MCMC methods | |
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| Classic BUGS | |
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| WinBUGS | |
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| Using WinBUGS: compound documents | |
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| Formatting data | |
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| Using the WinBUGS graphical interface | |
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| Doodles | |
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| Scripting | |
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| Interfaces with other software | |
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| R2WinBUGS | |
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| WBDev | |
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| OpenBUGS | |
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| Differences from WinBUGs | |
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| OpenBUGS on Linux | |
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| BRugs | |
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| Parallel computation | |
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| JAGS | |
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| Extensibility: modules | |
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| Language differences | |
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| Other differences from WinBUGS | |
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| Running JAGS from the command line | |
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| Running JAGS from R | |
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| BUGS language syntax | |
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| Introduction | |
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| Distributions | |
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| Standard distributions | |
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| Censoring and truncation | |
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| Non-standard distributions | |
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| Deterministic functions | |
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| Standard functions | |
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| Special functions | |
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| Add-on functions | |
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| Repetition | |
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| Multivariate quantities | |
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| Indexing | |
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| Functions as indices | |
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| Implicit indexing | |
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| Nested indexing | |
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| Data transformations | |
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| Commenting | |
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| Functions in BUGS | |
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| Standard functions | |
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| Trigonometric functions | |
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| Matrix algebra | |
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| Distribution utilities and model checking | |
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| Functionals and differential equations | |
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| Miscellaneous | |
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| Distributions in BUGS | |
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| Continuous univariate, unrestricted range | |
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| Continuous univariate, restricted to be positive | |
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| Continuous univariate, restricted to a finite interval | |
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| Continuous multivariate distributions | |
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| Discrete univariate distributions | |
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| Discrete multivariate distributions | |
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| Bibliography | |
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| Index | |