The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

Abstract

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis-Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature [27] where the target distribution is explored using a continuous-time non-reversible piecewise-deterministic Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently of higher "energy", than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper "local" bounces which only involve the state variables associated to a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high dimensional models and large data sets.

Automated learning with a probabilistic programming language: Birch

“…The model code is executed: when encountering a random variable in L it is simulated from the prior, and when encountering a random variable in O a cumulative weight is updated by multiplying in the likelihood of the given value. We have then simulated from the first product (5), and assigned a weight according to the second product (6).…”

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Coordinate sampler: a non-reversible Gibbs-like MCMC sampler

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Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems

“…In recent years, non-reversible MCMC algorithms have attracted a lot of attention, because of their favourable convergence and mixing properties; the literature on the matter has rapidly become large, here we refer the reader to e.g. [14,15,2,3,7] and references therein; however, to the best of our knowledge most of the papers on non-reversible MCMC so far have tested this new class of algorithms only on relatively simple target measures. Furthermore, the performance of non-reversible algorithms has been discussed almost exclusively in the case in which the measure is supported on the whole of R N .…”