Posterior Computation with the Gibbs Zig-Zag Sampler

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