Multilevel Monte Carlo in approximate Bayesian computation. Issue 3 (4th May 2019)

• Record Type: Journal Article
• Authors: Jasra, Ajay; Jo, Seongil; Nott, David; Shoemaker, Christine; Tempone, Raul
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 3(2019)
• Page Start: 346
• Page End: 360
• Publication Date: 2019-05-04
• Subjects: Approximate Bayesian computation -- multilevel Monte Carlo -- sequential Monte Carlo; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1566006
• Languages: English
• ISSNs: 0736-2994

Abstract

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.