PDMP Monte Carlo methods for piecewise-smooth densities

11/10/2021
by   Augustin Chevallier, et al.
0

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. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the Zig-Zag Process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise-deterministic Markov process with boundaries may be of independent interest.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/20/2019

Cores for Piecewise-Deterministic Markov Processes used in Markov Chain Monte Carlo

This article provides a tool for the analysis of Piecewise-deterministic...
08/26/2018

Hypercoercivity of Piecewise Deterministic Markov Process-Monte Carlo

In this paper we derive spectral gap estimates for several Piecewise Det...
12/27/2020

Adaptive Schemes for Piecewise Deterministic Monte Carlo Algorithms

The Bouncy Particle sampler (BPS) and the Zig-Zag sampler (ZZS) are cont...
08/26/2018

Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo

In this work, we establish L^2-exponential convergence for a broad class...
11/18/2020

Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods

We extend the hypocoercivity framework for piecewise-deterministic Marko...
10/22/2020

Reversible Jump PDMP Samplers for Variable Selection

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simu...
05/23/2019

The Skipping Sampler: A new approach to sample from complex conditional densities

We introduce the Skipping Sampler, a novel algorithm to efficiently samp...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.