Repository: Freie Universit├Ąt Berlin, Math Department

Nonasymptotic bounds for suboptimal importance sampling

Hartmann, C. and Richter, L. (2021) Nonasymptotic bounds for suboptimal importance sampling. arXive . pp. 1-26. (Submitted)

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Official URL: https://arxiv.org/pdf/2102.09606.pdf.

Abstract

Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notoriousquestion is how to design good proposal distributions. While in most cases optimal (zero-variance) estimatorsare theoretically possible, in practice only suboptimal proposal distributions are available and it can often beobserved numerically that those can reduce statistical performance significantly, leading to large relative errorsand therefore counteracting the original intention. In this article, we provide nonasymptotic lower and upperbounds on the relative error in importance sampling that depend on the deviation of the actual proposal fromoptimality, and we thus identify potential robustness issues that importance sampling may have, especially in highdimensions. We focus on path sampling problems for diffusion processes, for which generating good proposalscomes with additional technical challenges, and we provide numerous numerical examples that support ourfindings

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2563
Deposited By: Monika Drueck
Deposited On:27 Apr 2021 13:48
Last Modified:14 Mar 2022 14:21

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