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Monte Carlo fusion

Lookup NU author(s): Dr Murray Pollock

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Abstract

© Applied Probability Trust 2019.In this paper we propose a new theory and methodology to tackle the problem of unifying Monte Carlo samples from distributed densities into a single Monte Carlo draw from the target density. This surprisingly challenging problem arises in many settings (for instance, expert elicitation, multiview learning, distributed 'big data' problems, etc.), but to date the framework and methodology proposed in this paper (Monte Carlo fusion) is the first general approach which avoids any form of approximation error in obtaining the unified inference. In this paper we focus on the key theoretical underpinnings of this new methodology, and simple (direct) Monte Carlo interpretations of the theory. There is considerable scope to tailor the theory introduced in this paper to particular application settings (such as the big data setting), construct efficient parallelised schemes, understand the approximation and computational efficiencies of other such unification paradigms, and explore new theoretical and methodological directions.

Publication metadata

Author(s): Dai H, Pollock M, Roberts G

Publication type: Article

Publication status: Published

Journal: Journal of Applied Probability

Year: 2019

Volume: 56

Issue: 1

Pages: 174-191

Print publication date: 01/03/2019

Online publication date: 12/07/2019

Acceptance date: 02/04/2016

ISSN (print): 0021-9002

ISSN (electronic): 1475-6072

Publisher: Applied Probability Trust

URL: https://doi.org/10.1017/jpr.2019.12

DOI: 10.1017/jpr.2019.12

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