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Sampling using Adaptive Regenerative Processes

McKimm, Hector; Wang, Andi Q.; Pollock, Murray; Robert, Christian P.; Roberts, Gareth O. (2022), Sampling using Adaptive Regenerative Processes. https://basepub.dauphine.psl.eu/handle/123456789/24097

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
34
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Author(s)
McKimm, Hector
Department of Statistics [Warwick]
Wang, Andi Q.
Department of Statistics [Warwick]
Pollock, Murray
UNIVERSITY OF NEWCASTLE GBR
Robert, Christian P.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Roberts, Gareth O.
Department of Statistics [Warwick]
Abstract (EN)
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. 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, which can drastically reduce computational cost. We establish convergence of this self-reinforcing process and explore its effectiveness at sampling from a number of target distributions. The examples show that our adaptive method allows regeneration-enriched Brownian Motion to be used to sample from target distributions for which simulation under a fixed regeneration distribution is computationally intractable.
Subjects / Keywords
Adaptive algorithm; Markov process; MCMC; Normalizing constant; Regeneration distribution; Restore sampler; Sampling; Simulation