Three Short Papers on Sampling-Based Inference: 1. How Many Iterations in the Gibbs Sampler 2. Model Determination. 3. Spatial Statistics.

摘要

This technical report consists of three short papers on Monte Carlo Markov chain inference. The first paper, How many iterations in the Gibbs sampler, proposes an easily implemented method for determining the total number of iterations required to estimate probabilities and quantiles of the posterior distribution, and also the number of initial iterations that should be discarded to allow for burn-in. The second paper discusses model determination via predictive distributions. The paper advocates the standard Bayesian procedure that uses Bayes factors, and points out that this can be implemented quite easily using sampling-based methods. The third paper discusses issues in spatial statistics that use sampling-based methods. Several issues in the Bayesian image restoration approach are discussed: the modeling of spatial dependence, allowing for model uncertainty, the improper posterior distributions that arise in hierarchical Bayes modeling, and the modeling of local dependence between counts when it cannot be assumed that the observations are independent given the true rates.