Statistics Seminars Schedule
Venue: Huxley 139
2-3pm: Sergios Agapiou (Warwick)
Title: Practical unbiased Monte Carlo for intractable models
Abstract:
We will consider the problem of unbiased estimation of expectations with respect to measures which are intractable in the sense that they are only available as limits of distributions. We will build on recent work by Peter Glynn and Chang-han Rhee. In particular, we will first discuss how to remove the bias introduced by discretization when computing expectations with respect to Gaussian measures in function space. Then, we will discuss how to remove the bias due to burn-in when computing expectations with respect to limiting distributions of Markov chains. Finally, we will briefly sketch a method of combining in order to perform estimation of expectations with respect to limiting distributions of Markov chains in function space, which is unbiased with respect to both discretization and burn-in. This is joint work with Gareth Roberts and Sebastian Vollmer, contained in arXiv:1411.7713
3-3:20: coffee break
3:20-4:20 Andrew Duncan (Imperial)
Title: Accelerating convergence and reducing variance for diffusions
Abstract: MCMC provides a powerful and general approach for generating samples from a high-dimensional target probability distribution, known up to a normalizing constant. There are infinitely many Markov processes whose invariant measure equals a given target distribution. The natural question is whether a Markov process can be chosen to generate samples of the target distribution as efficiently as possible. It has been previously observed that adding an appropriate nonreversible perturbation to a reversible Markov process will improve its performance. In this talk, I will describe some recent results which characterise the effect of adding a nonreversible drift to an overdamped Langevin sampler, in terms of rate of convergence to equilibrium and asymptotic variance. For Gaussian target distributions, the effect can be quantified explicitly, allowing one to identify an optimal non-reversible perturbation, both for maximising rate of convergence to equilibrium and minimising the asymptotic variance. For more general target distributions, we demonstrate how the effect of the nonreversible drift can be expressed in terms of the spectrum of the generator of the process. Theoretical results are supplemented by simulations. Joint work with T. Lelievre and G. Pavliotis.