Monte Carlo methods based on novel classes of regeneration-enriched Markov processes

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Abstract

Enriching some underlying continuous-time Markov process with regenerations from a fixed regeneration distribution µ at a particular regeneration rate Ƙ results in a Markov process that has a target distribution π as its invariant distribution. Firstly, we introduce a method for adapting the regeneration distribution, which allows a significantly smaller regeneration rate to be used, which makes simulation feasible for a wider range of target distributions. The regeneration distribution is adapted on-the-fly, by adding point masses to it. Secondly, we show that a class of non- π -invariant jump processes, which are defined on an augmented statespace and have a jump chain transition kernel corresponding to a deterministic, invertible mapping, may be enriched with regenerations so that the resulting process is π -invariant. Since the underlying jump process does not need to be π invariant, its dynamics may be chosen to use gradient information to guide the process to areas of high probability mass, which makes the sampler a promising algorithm for multi-modal target distributions.

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