I will discuss a class of Markov processes comprising local dynamics governed by a fixed Markov process which are enriched with regenerations from a fixed distribution at a state-dependent rate. We give conditions under which such processes possess a given target distribution as their invariant measures, thus making them suitable as the basis of a new Monte Carlo sampling framework. The resulting Restore Sampler has several desirable properties: simplicity, lack of rejections, nonreversibility, regenerations and a potential coupling from the past implementation. The sampler can also be used as a recipe for introducing rejection-free moves into existing Markov Chain Monte Carlo samplers in continuous time.
Joint work with Murray Pollock, Gareth Roberts and David Steinsaltz.