Concave-Convex PDMP-based sampling

TL;DR

This paper introduces a novel concave-convex adaptive thinning method for efficient simulation of PDMP-based samplers in Bayesian inference, improving computational efficiency and ease of implementation.

Contribution

It proposes the CC-PDMP approach, leveraging concave-convex decompositions for better bounds, facilitating local PDMP simulation, and providing an R package for practical use.

Findings

Outperforms existing PDMP simulation methods.

Enables efficient local PDMP sampling with conditional independence.

Provides a flexible, easy-to-implement framework for PDMP-based sampling.

Abstract

Recently non-reversible samplers based on simulating piecewise deterministic Markov processes (PDMPs) have shown potential for efficient sampling in Bayesian inference problems. However, there remains a lack of guidance on how to best implement these algorithms. If implemented poorly, the computational costs of simulating event times can out-weigh the statistical efficiency of the non-reversible dynamics. Drawing on the adaptive rejection literature, we propose the concave-convex adaptive thinning approach for simulating a piecewise deterministic Markov process (CC-PDMP). This approach provides a general guide for constructing bounds that may be used to facilitate PDMP-based sampling. A key advantage of this method is its additive structure - adding concave-convex decompositions yields a concave-convex decomposition. This facilitates swapping priors, simple implementation and computationally efficient thinning. In particular, our approach is well suited to local PDMP simulation where known conditional independence of the target can be exploited for potentially huge computational gains. We provide an R package for implementing the CC-PDMP approach and illustrate how our method outperforms existing approaches to simulating events in the PDMP literature.