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 efficiency. This article introduces a new method, called bound and collapse (BC) to tackle these problems. BC first bounds the possible estimates consistent with the available information and then collapses these bounds to a point estimate using information about the pattern of missing data. Deterministic approximations of the variance and of the posterior distribution are proposed, and their accuracy is compared to stochastic approximations in a real dataset of polling data subject to nonresponse.