Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on collection $N$ interacting auxiliary chains targeting tempered versions the target distribution improve exploration state-space. We provide here new perspective these highly parallel algorithms and their tuning by identifying formalizing sharp divide in behaviour performance reversible versus non-reversible PT schemes. show theoretically empirically that dominates its counterparts identify distinct scaling limits for schemes, former being piecewise-deterministic process latter diffusion. These results exploited optimal annealing schedule develop an iterative scheme approximating this schedule. wide range numerical examples supporting our theoretical methodological contributions. The proposed methodology is applicable from $\pi$ with density $L$ respect reference $\pi_0$ compute normalizing constant. A typical use case when prior distribution, likelihood function corresponding posterior.