Sampling using Adaptive Regenerative Processes
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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.
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