I work mainly on methods for Bayesian computation, motivated by applications. Much of my computational work has been motivated by the problems posed by intractable likelihoods, which are encountered in inference for: state-space models; models specified in a an unnormalised form, which have an intractable partition function; and in stochastic models specified as a simulation algorithm. I work on approximate Bayesian computation (ABC), particle MCMC, and related methods. I am also interested in sequential inference in several different settings, including analysing genetic data, time-frequency analysis, and Bayesian model comparison. Other work on Bayesian computation is found here.