Posterior computation with the Gibbs zig-zag sampler

Sachs, Matthias and Sen, Deborshee and Lu, Jianfeng and Dunson, David (2023) Posterior computation with the Gibbs zig-zag sampler. Bayesian Analysis, 18 (3). pp. 909-927. ISSN 1936-0975

Abstract

An intriguing new class of piecewise deterministic Markov processes (PDMPs) has recently been proposed as an alternative to Markov chain Monte Carlo (MCMC). 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.