Abstract

The pseudo-marginal MCMC algorithm is a powerful tool for exploring the posterior distribution when only unbiased stochastic estimates of the target density are available. In many situations, although there is no closed-form expression for this density, computationally cheap deterministic estimates are also available; one can then use a delayed-acceptance strategy for exploiting these cheap approximations.

As powerful as they are, the use of such algorithms are difficult in practice: it involves tuning the MCMC proposals and choosing the computational budget that one is willing to invest in the creation of the unbiased estimates while taking into account the quality of the cheap deterministic approximations. In this talk we discuss how high-dimensional asymptotic results can help in the tuning of these delayed-acceptance pseudo-marginal MCMC algorithms.

This is joint work with Chris Sherlock and Andrew Golightly.