Sequential stratified splitting for efficient Monte Carlo integration. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Vaisman, Radislav
• Is Part Of: Sequential analysis. Volume 40:Issue 3(2021)
• Page Start: 314
• Page End: 335
• Publication Date: 2021-07-03
• Subjects: Algorithmic efficiency -- Markov chain Monte Carlo -- multidimensional integration -- multilevel splitting -- sequential Monte Carlo; 60J20 -- 65C05 -- 65C10; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2021.1940493
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: The efficient evaluation of high-dimensional integrals is important from both theoretical and practical points of view. In particular, multidimensional integration plays a central role in Bayesian inference, statistical physics, data science, and machine learning. However, due to the curse of dimensionality, deterministic numerical methods are inefficient in the high-dimensional setting. Consequentially, for many practical problems one must resort to approximate estimation techniques such as Monte Carlo methods. In this article, we introduce a novel sequential Monte Carlo algorithm called stratified splitting. The method provides unbiased estimates and can handle various integrand types including indicator functions, which are important for rare-event probability estimation problems. We provide rigorous analysis of the efficiency of the proposed method and present a numerical demonstration of the algorithmic performance when applied to practical application domains. Our numerical experiments suggest that the stratified splitting method is capable of delivering accurate results for a variety of integration problems while requiring reasonable computational effort.