1. Variational Methods TCD Interests Simon Wilson

2. Background We are new to this area of research – so we can’t say very much about it – but we’re enthusiastic! Our interest is in the use of variational methods for implementing Bayesian inference; Current literature in statistics concentrates on the “variational Bayes” approach to approximating posterior distributions; This is an iterative procedure: –It tends to be faster than MCMC –It tends to underestimate the posterior variance

3. Variational Bayes Approximation of a posterior distribution p(  | data) by some other (more amenable) function q(  ); Objective function - KL distance “Mean field approximation” usually assumed: iterative updating of each q i developed

4. Research Questions How to exploit other aspects of variational methods to propose new approximative techniques for Bayesian inference; Can we exploit parallel computing for high- dimensional problems? –Variational Bayes not necessarily good for this (it’s iterative) Motivate through image applications; Funding proposals currently in progress – hope to have Ph.D. student from October 06 (will know by May).