Posterior computation with the Gibbs zig-zag sampler

TL;DR

This paper introduces Gibbs zig-zag samplers, a new class of PDMPs combining zig-zag and MCMC updates, enabling efficient posterior sampling in high-dimensional models with theoretical guarantees.

Contribution

It proposes a novel PDMP framework that integrates zig-zag and MCMC updates for improved posterior sampling in complex models.

Findings

Demonstrates flexibility on logistic models with shrinkage priors

Provides conditions for geometric ergodicity

Establishes validity of a central limit theorem

Abstract

An intriguing new class of piecewise deterministic Markov processes (PDMPs) has recently been proposed as an alternative to Markov chain Monte Carlo (MCMC). In order to facilitate the application to a larger class of problems, we propose a new class of PDMPs termed Gibbs zig-zag samplers, which allow parameters to be updated in blocks with a zig-zag sampler applied to certain parameters and traditional MCMC-style updates to others. We demonstrate the flexibility of this framework on posterior sampling for logistic models with shrinkage priors for high-dimensional regression and random effects and provide conditions for geometric ergodicity and the validity of a central limit theorem.