Bayesian Inference with Missing Data Using Bound and Collapse

Current Bayesian methods to estimate conditional probabilities from samples with missing data pose serious problems of robustness and computational eeciency. This paper introduces a new method, called Bound and Collapse (bc), able to overcome these problems. When no information is available on the pattern of missing data, bc returns bounds on the possible estimates consistent with the available information. These bounds can be then collapsed to a point estimate using information about the pattern of missing data, if any. Approximations of the variance and of the posterior distribution are proposed, and their accuracy is compared to approximations based on alternative methods in a real data set of polling data subject to non-response.