Abstract: Likelihood and Bayesian inference for incomplete-data problems tend to involve computational complications. In Bayesian inference, for example, simulation-based methods such as Markov chain Monte Carlo represent one approach to dealing with such difficulties. The talk will describe a more deterministic approach, based on so-called variational approximations. These have been developed in the computer science literature and versions of them for likelihood analysis and Bayesian analysis will be described in the talk. Application to the analysis of mixture models and extensions thereof will be discussed, as will general issues concerning the theoretical properties of the methods.