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. To appear 2024 in SIAM/ASA Journal on Uncertainty Quantification . (In Press)

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Official URL: https://doi.org/10.48550/arXiv.2102.09606

Abstract

Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. In this article, we provide nonasymptotic lower and upper bounds on the relative error in importance sampling that depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We focus on path sampling problems for diffusion processes, for which generating good proposals comes with additional technical challenges, and we provide numerous numerical examples that support our findings.

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:23 Feb 2024 12:11

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