TY - JOUR

T1 - Concave-Convex PDMP-based sampling

AU - Sutton, Matthew

AU - Fearnhead, Paul

PY - 2023/10/2

Y1 - 2023/10/2

N2 - Recently nonreversible 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 outweigh the statistical efficiency of the nonreversible dynamics. Drawing on the adaptive rejection literature, we propose the concave-convex adaptive thinning approach for simulating a piecewise deterministic Markov process, which we call 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 makes the construction of bounds modular, as given a concave-convex decomposition for a class of likelihoods and a family of priors, they can be combined to construct bounds for the posterior. We show that constructing our bounds is simple and leads to computationally efficient thinning. Our approach is well suited to local PDMP simulation where conditional independence of the target can be exploited for potentially huge computational gains. We provide an R package and compare with existing approaches to simulating events in the PDMP literature. Supplementary materials for this article are available online.

AB - Recently nonreversible 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 outweigh the statistical efficiency of the nonreversible dynamics. Drawing on the adaptive rejection literature, we propose the concave-convex adaptive thinning approach for simulating a piecewise deterministic Markov process, which we call 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 makes the construction of bounds modular, as given a concave-convex decomposition for a class of likelihoods and a family of priors, they can be combined to construct bounds for the posterior. We show that constructing our bounds is simple and leads to computationally efficient thinning. Our approach is well suited to local PDMP simulation where conditional independence of the target can be exploited for potentially huge computational gains. We provide an R package and compare with existing approaches to simulating events in the PDMP literature. Supplementary materials for this article are available online.

KW - stat.ME

U2 - 10.1080/10618600.2023.2203735

DO - 10.1080/10618600.2023.2203735

M3 - Journal article

VL - 32

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 4

ER -