Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments

Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods from spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model with informative priors, and in the Tobit-censored regression model. Keywords and phrases: Data augmentation, Gibbs sampling, Mixed estimation, Monte Carlo integration, Tobit model This paper was prepared as an invited presentation at the Fourth Valencia International Meeting on Bayesian Statistics, Peñiscola, Spain, April 15-20, 1991. Financial support from National Science Foundation Grant SES-8908365 and res...