Sampling using Adaptive Regenerative Processes

Hector Mckimm (1) , Andi Q Wang (1) , Murray Pollock (2) , Christian P Robert (3, 4) , Gareth O Roberts (1)

1 Department of Statistics [Warwick]
2 Newcastle University [Newcastle]
3 Université Paris Dauphine-PSL
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Enriching Brownian Motion with regenerations from a fixed regeneration distribution $\mu$ at a particular regeneration rate $\kappa$ results in a Markov process that has a target distribution $\pi$ 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.

Mots clés: Adaptive algorithm Markov process MCMC Normalizing constant Regeneration distribution Restore sampler Sampling Simulation; Adaptive algorithm; Markov process; MCMC; Normalizing constant; Regeneration distribution; Restore sampler; Sampling; Simulation

Domaines: Statistiques [stat]; Modélisation et simulation; Probabilités [math.PR]

Hector Mckimm, Andi Q Wang, Murray Pollock, Christian P Robert, Gareth O Roberts. Sampling using Adaptive Regenerative Processes. 2022. ⟨hal-03911766⟩