Distributed and Adaptive Darting Monte Carlo through Regenerations

Darting Monte Carlo (DMC) is a MCMC procedure designed to effectively mix between multiple modes of a probability distribution. We propose an adaptive and distributed version of this method by using regenerations. This allows us to run multiple chains in parallel and adapt the shape of the jump regions as well as all other aspects of the Markov chain on the fly. We show that this significantly improves the performance of DMC because 1) a population of chains has a higher chance of finding the modes in the distribution, 2) jumping between modes becomes easier due to the adaptation of their shapes, 3) computation is much more efficient due to parallelization across multiple processors. While the curse of dimensionality is a challenge for both DMC and regeneration, we find that their combination ameliorates this issue slightly.