Practical Use of MCMC Methods: Lessons from a Case Study

This paper uses the analysis of a data set to examine a number of issues in Bayesian statistics and the application of MCMC methods. The data concern the selectivity of fishing nets and logistic regression is used to relate the size of a fish to the probability it will be retained or escape from a trawl net. Hierarchical models relate information from different trawls and posterior distributions are determined using MCMC. Centring data is shown to radically reduce autocorrelation in chains and Rao‐Blackwellisation and chain‐thinning are found to have little effect on parameter estimates. The results of four convergence diagnostics are compared and the sensitivity of the posterior distribution to the prior distribution is examined using a novel method. Nested models are fitted to the data and compared using intrinsic Bayes factors, pseudo‐Bayes factors and credible intervals.