Posterior Computation with the Gibbs Zig-Zag Sampler

Matthias Sachs, Deborshee Sen, Jianfeng Lu, David Dunson

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1 Citation (SciVal)

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.

Original languageEnglish
Pages (from-to)909-927
Number of pages19
JournalBayesian Analysis
Volume18
Issue number3
DOIs
Publication statusPublished - 30 Sept 2023

Bibliographical note

Funding Information:
∗DS and DD acknowledge support from National Science Foundation grant 1546130. MS and DS acknowledge support from grant DMS-1638521 from SAMSI. The work of JL is supported in part by the National Science Foundation via grants DMS-1454939 and CCF-1934964 (Duke TRIPODS). †School of Mathematics, University of Birmingham, [email protected] ‡Department of Mathematical Sciences, University of Bath, [email protected] §Department of Mathematics, Duke University, [email protected] ¶Department of Statistical Science, Duke University, [email protected] ‖The two authors contributed equally to this article. ∗∗Corresponding author.

Keywords

  • Gibbs sampler
  • Markov chain Monte Carlo
  • non-reversible
  • piecewise deterministic Markov process
  • sub-sampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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