Ben Amar, E, Ben Rached, N, Hai-Ali, A-L et al. (1 more author) (2023) State-dependent Importance Sampling for Estimating Expectations of Functionals of Sums of Independent Random Variables. Statistics and Computing, 33. 40. ISSN 0960-3174
Abstract
Estimating the expectations of functionals applied to sums of random variables (RVs) is a well-known problem encountered in many challenging applications. Generally, closed-form expressions of these quantities are out of reach. A naive Monte Carlo simulation is an alternative approach. However, this method requires numerous samples for rare event problems. Therefore, it is paramount to use variance reduction techniques to develop fast and efficient estimation methods. In this work, we use importance sampling (IS), known for its efficiency in requiring fewer computations to achieve the same accuracy requirements. We propose a state-dependent IS scheme based on a stochastic optimal control formulation, where the control is dependent on state and time. We aim to calculate rare event quantities that could be written as an expectation of a functional of the sums of independent RVs. The proposed algorithm is generic and can be applied without restrictions on the univariate distributions of RVs or the functional applied to the sum. We apply this approach to the log-normal distribution to compute the left tail and cumulative distribution of the ratio of independent RVs. For each case, we numerically demonstrate that the proposed state-dependent IS algorithm compares favorably to most well-known estimators dealing with similar problems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Monte Carlo, rare event, importance sampling, stochastic optimal control |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Feb 2025 15:39 |
Last Modified: | 21 Feb 2025 15:39 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s11222-022-10202-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:192941 |