Debiasing piecewise deterministic Markov process samplers using couplings

Monte Carlo methods—such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers—provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in alternatives to this asymptotic regime, in particular in constructing estimators that are exact in the limit of an infinite number of computing processors, rather than in the limit of an infinite number of Markov iterations. In particular, coupled MCMC estimators remove the non-asymptotic bias, resulting in MCMC estimators that can be embarrassingly parallelized. In this work, we extend these estimators to the continuous-time context and derive couplings for the bouncy, the boomerang, and the coordinate samplers. Some preliminary empirical results are included that demonstrate the reasonable scaling of our method with the dimension of the target.