Optimal potential functions for the interacting particle system method

Chraibi Hassane (), Dutfoy Anne (), Galtier Thomas () and Garnier Josselin ()
Additional contact information
Chraibi Hassane: Électricité de France (EDF), PERICLES Department, 7 Boulevard Gaspard Monge, 91120Palaiseau, France
Dutfoy Anne: Électricité de France (EDF), PERICLES Department, 7 Boulevard Gaspard Monge, 91120Palaiseau, France
Galtier Thomas: CMAP, École polytechnique, Institut Polytechnique de Paris, 91128PalaiseauCedex, France
Garnier Josselin: CMAP, École polytechnique, Institut Polytechnique de Paris, 91128PalaiseauCedex, France

Monte Carlo Methods and Applications, 2021, vol. 27, issue 2, 137-152

Abstract: The assessment of the probability of a rare event with a naive Monte Carlo method is computationally intensive, so faster estimation or variance reduction methods are needed. We focus on one of these methods which is the interacting particle system (IPS) method. The method is not intrusive in the sense that the random Markov system under consideration is simulated with its original distribution, but selection steps are introduced that favor trajectories (particles) with high potential values. An unbiased estimator with reduced variance can then be proposed. The method requires to specify a set of potential functions. The choice of these functions is crucial because it determines the magnitude of the variance reduction. So far, little information was available on how to choose the potential functions. This paper provides the expressions of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method and it proposes recommendations for the practical design of the potential functions.

Keywords: Rare event simulation; interacting particle system; sequential Monte Carlo samplers particle filters (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2021-2086 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:27:y:2021:i:2:p:137-152:n:2

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2021-2086

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().