Advanced Multilevel Monte Carlo Methods

Jasra, Ajay; Law, Kody; Suciu, Carina

doi:10.1111/insr.12365

Title: Advanced Multilevel Monte Carlo Methods

Journal Article · Tue Mar 03 00:00:00 EST 2020 · International Statistical Review

DOI:https://doi.org/10.1111/insr.12365· OSTI ID:1862171

^[1]; Law, Kody ^[2]; Suciu, Carina ^[1]

King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)
Univ. of Manchester (United Kingdom)

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and more expensive. Additionally, using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider some Markov chain Monte Carlo and sequential Monte Carlo methods, which have been introduced in the literature, and we describe different strategies that facilitate the application of MLMC within these methods.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725; 32102582

OSTI ID:: 1862171

Journal Information:: International Statistical Review, Vol. 88, Issue 3; ISSN 0306-7734

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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