Markov Chain Monte Carlo (MCMC) simulation as a method for practical
calculation of Bayesian results. The Gibbs sampler.
Metropolis-Hastings sampling. Metropolis-within-Gibbs sampling.
Computer tools, e.g., BUGS,S+, R.
Bayesian point and interval parameter estimation. Bayesian credible
intervals. Comparison with frequentist parameter estimation and
confidence intervals. Bayesian inference on Gaussian likelihoods.
Maximum Likelihood estimation as a Bayesian approximation. Laplace's
approximation. Bayesian inference in non-Gaussian cases, e.g.,
Poisson, Cauchy, and arbitrary distributions. Linear and nonlinear
models. Errors-in-variables models.
Bayesian hypothesis testing. Comparison with frequentist hypothesis
testing. Model selection and model averaging. Reversible jump MCMC
for models of variable size. Approximations, e.g., AIC, BIC.
Philosophical issues, likelihood principle, and the Bayesian Ockham's
Razor.
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