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.
Funding Statement
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).
Citation
Matthias Sachs. Deborshee Sen. Jianfeng Lu. David Dunson. "Posterior Computation with the Gibbs Zig-Zag Sampler." Bayesian Anal. 18 (3) 909 - 927, September 2023. https://doi.org/10.1214/22-BA1319
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