Browse by author
Lookup NU author(s): Professor Murray Pollock
Full text for this publication is not currently held within this repository. Alternative links are provided below where available.
© 2025, Bernoulli Society for Mathematical Statistics and Probability. All rights reserved.Enriching Brownian motion with regenerations from a fixed regeneration distribution μ at a particular regeneration rate κ results in a Markov process that has a target distribution π as its invariant distribution. For the purpose of Monte Carlo inference, implementing such a scheme requires firstly selection of regeneration distribution μ, and secondly computation of a specific constant C. Both of these tasks can be very difficult in practice for good performance. We introduce a method for adapting the regeneration distribution, by adding point masses to it. This allows the process to be simulated with as few regenerations as possible and obviates the need to find said constant C. Moreover, the choice of fixed μ is replaced with the choice of the initial regeneration distribution, which is considerably less difficult. We establish convergence of this resulting self-reinforcing process and explore its effectiveness at sampling from a number of target distributions. The examples show that adapting the regeneration distribution guards against poor choices of fixed regeneration distribution and can reduce the error of Monte Carlo estimates of expectations of interest, especially when π is skewed.
Author(s): McKimm H, Wang A, Pollock M, Robert C, Roberts G
Publication type: Article
Publication status: Published
Journal: Bernoulli
Year: 2025
Volume: 31
Issue: 1
Pages: 509-536
Print publication date: 01/02/2025
Online publication date: 30/10/2024
Acceptance date: 02/04/2018
ISSN (print): 1350-7265
ISSN (electronic): 1573-9759
Publisher: Bernoulli Society for Mathematical Statistics and Probability
URL: https://doi.org/10.3150/24-BEJ1737
DOI: 10.3150/24-BEJ1737
Altmetrics provided by Altmetric
