PDMP Monte Carlo methods for piecewise-smooth densities

Understand

There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes.

• However existing algorithms can only be used if the target distribution of interest is differentiable everywhere.
• The key to adapting these algorithms so that they can sample from to densities with discontinuities is defining appropriate dynamics for the process when it hits a discontinuity.
• We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the Bouncy Particle Sampler, the Coordinate Sampler and the Zig-Zag Process.