Colloq: Nick Whiteley

Date: 

Monday, October 31, 2016, 4:15pm to 5:15pm

Location: 

Science Center Rm. 300H

Log-concavity and importance sampling in high dimensions

Importance sampling is one of the elementary Monte Carlo methods for approximating expectations with respect to a 'target' distribution whose normalizing constant is unknown. The idea is simply to draw samples from some other distribution which dominates the target, then approximate the expectation of interest using appropriately weighted sample averages.

Direct application of this idea can perform badly in high dimensions, and for even very simple examples involving densities on R^d, computational effort much be increased exponentially with d in order to prevent the Monte Carlo variance of importance sampling approximations from exploding.

The purpose of this talk is to illustrate that when the basic importance sampling idea is applied in a more sophisticated manner, which involves an importance sampling correction between the laws of certain diffusion processes constructed in terms of the target distribution, the exponential growth of computational cost with dimension can be avoided. One of the key assumptions is log-concavity of the target distribution, which is leveraged by showing that it furnishes the diffusions in question with some appealing 'dimension-free' ergodic properties.

This is joint work with Christophe Andrieu and James Ridgeway.