Multilevel Monte Carlo in approximate Bayesian computation

Ajay Jasra; Seongil Jo; David Nott; Christine Shoemaker; Raul Tempone

doi:10.1080/07362994.2019.1566006

Multilevel Monte Carlo in approximate Bayesian computation

Ajay Jasra^*, Seongil Jo, David Nott, Christine Shoemaker, Raul Tempone

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

Original language	English (US)
Pages (from-to)	346-360
Number of pages	15
Journal	Stochastic Analysis and Applications
Volume	37
Issue number	3
DOIs	https://doi.org/10.1080/07362994.2019.1566006
State	Published - May 4 2019

Keywords

Approximate Bayesian computation
multilevel Monte Carlo
sequential Monte Carlo

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1080/07362994.2019.1566006

Cite this

@article{ff37bd0c4668456887c7eede8ec2c828,

title = "Multilevel Monte Carlo in approximate Bayesian computation",

abstract = "In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.",

keywords = "Approximate Bayesian computation, multilevel Monte Carlo, sequential Monte Carlo",

author = "Ajay Jasra and Seongil Jo and David Nott and Christine Shoemaker and Raul Tempone",

note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Taylor & Francis Group, LLC.",

year = "2019",

month = may,

day = "4",

doi = "10.1080/07362994.2019.1566006",

language = "English (US)",

volume = "37",

pages = "346--360",

journal = "Stochastic Analysis and Applications",

issn = "0736-2994",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - Multilevel Monte Carlo in approximate Bayesian computation

AU - Jasra, Ajay

AU - Jo, Seongil

AU - Nott, David

AU - Shoemaker, Christine

AU - Tempone, Raul

PY - 2019/5/4

Y1 - 2019/5/4

N2 - In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

AB - In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

KW - Approximate Bayesian computation

KW - multilevel Monte Carlo

KW - sequential Monte Carlo

UR - http://www.scopus.com/inward/record.url?scp=85060891877&partnerID=8YFLogxK

U2 - 10.1080/07362994.2019.1566006

DO - 10.1080/07362994.2019.1566006

M3 - Article

AN - SCOPUS:85060891877

SN - 0736-2994

VL - 37

SP - 346

EP - 360

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 3

ER -

Multilevel Monte Carlo in approximate Bayesian computation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this