Felipe Medina Aguayo (University of Warwick): The Pseudo-Marginal Approach to MCMC

Metropolis-Hastings algorithm emerged as a useful and powerful simulation tool for many settings in different areas. However when we do not have an analytic expression for the target density, we may need to appeal to an algorithm on an extended space. This could easily turn into a high-dimensional problem, possibly leading to mixing and convergence complications. The use of importance sampling estimates for the unknown target distribution provides a second alternative. Even though this approximation introduces a bias, a simple modification of this idea will eliminate such error. MCWM and GIMH algorithms are presented, as well as respective extensions within a particle MCMC context.

Joint work with Gareth Roberts, Anthony Lee