Automatic Zig-Zag sampling in practice

Abstract Novel Monte Carlo methods to generate samples from a target distribution, such as posterior Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs), non-reversible continuous-time processes, are developing into their own research branch, thanks important properties (e.g., super-efficiency). Nevertheless, practice has not caught up with theory this field, and use of PDMPs solve applied problems is widespread. This might be due, firstly, several implementational challenges that PDMP-based samplers present and, secondly, lack papers showcase implementations settings. Here, we address both these issues using one most promising PDMPs, Zig-Zag sampler, an archetypal example. After explanation key elements its implementation exposed addressed. Specifically, formulation algorithm draws distribution interest provided. Notably, only requirement closed-form differentiable function evaluate log-target density interest, unlike previous implementations, no further information needed. The performance evaluated against canonical Hamiltonian Carlo, it proven competitive, simulation real-data Lastly, demonstrate super-efficiency property, i.e. ability draw independent sample at lesser cost than evaluating likelihood all data, can obtained practice.