AUEB Stats Seminars 28/3/2023: Can independent Metropolis samplers beat Monte Carlo? by Petros Dellaportas (Department of Statistics, AUEB & UCL)

AUEB STATS SEMINARS 2023

Petros Dellaportas
Department of Statistics, AUEB & UCL

Title: Can independent Metropolis samplers beat Monte Carlo?

TUESDAY 28/3/2023
13:00

Room Τ103, New AUEB Building

ABSTRACT

Assume that we would like to estimate the expected value of a function f with respect to a density π by using an importance density function q. We prove that if π and q are close enough under KL divergence, an independent Metropolis sampler estimator that obtains samplers from π with proposal density q, enriched with a variance reduction computational strategy based on control variates, achieves smaller asymptotic variance than the one from crude Monte Carlo. We illustrate our results in challenging option pricing problems that require Monte Carlo estimation. Furthermore, we propose an automatic sampling methodology based on adaptive independent Metropolis and we demonstrate its applicability in option pricing and Bayesian inference problems.