Reversible Jump PDMP Samplers for Variable Selection

TL;DR

This paper introduces reversible jump PDMP samplers that enable efficient Bayesian variable selection by jointly exploring model space and parameters, overcoming limitations of existing PDMP methods.

Contribution

It develops a general framework for reversible jump PDMP samplers that incorporate trans-dimensional moves for variable selection, enhancing mixing and efficiency over traditional methods.

Findings

Samplers exhibit better mixing than standard MCMC.

Empirical results show higher efficiency than gradient-based approaches.

Framework is applicable to various PDMP samplers.

Abstract

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and can use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers can only sample from posterior densities that are differentiable almost everywhere, which precludes their use for model choice. Motivated by variable selection problems, we show how to develop reversible jump PDMP samplers that can jointly explore the discrete space of models and the continuous space of parameters. Our framework is general: it takes any existing PDMP sampler, and adds two types of trans-dimensional moves that allow for the addition or removal of a variable from the model. We show how the rates of these trans-dimensional moves can be calculated so that the sampler has the correct invariant distribution. Simulations show that the new samplers can mix better than standard MCMC algorithms. Our empirical results show they are also more efficient than gradient-based samplers that avoid model choice through use of continuous spike-and-slab priors which replace a point mass at zero for each parameter with a density concentrated around zero.