Σεμινάριο: "Can independent Metropolis samplers beat Monte Carlo?"

ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ ΜΑΡΤΙΟΣ 2023

Ομιλητής: Πέτρος Δελλαπόρτας, Τμήμα Στατιστικής, Οικονομικό Πανεπιστήμιο Αθηνών & UCL

Can independent Metropolis samplers beat Monte Carlo?

ΑΙΘΟΥΣΑ Τ103, ΝΕΟ ΚΤΙΡΙΟ ΟΠΑ

ΠΕΡΙΛΗΨΗ

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.