Cores for Piecewise-Deterministic Markov Processes used in Markov Chain Monte Carlo
| Autor: | Peter Holderrieth |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Markov chain Stochastic process Probability (math.PR) Markov process Markov chain Monte Carlo Mathematics - Statistics Theory Statistics Theory (math.ST) Feller process Statistics - Computation Hybrid Monte Carlo symbols.namesake FOS: Mathematics symbols Applied mathematics Piecewise-deterministic Markov process Statistics Probability and Uncertainty Martingale (probability theory) Computation (stat.CO) Mathematics - Probability Mathematics |
| Popis: | We show fundamental properties of the Markov semigroup of recently proposed MCMC algorithms based on Piecewise-deterministic Markov processes (PDMPs) such as the Bouncy Particle Sampler, the Zig-Zag process or the Randomized Hamiltonian Monte Carlo method. Under assumptions typically satisfied in MCMC settings, we prove that PDMPs are Feller and that their generator admits the space of infinitely differentiable functions with compact support as a core. As we illustrate via martingale problems and a simplified proof of the invariance of target distributions, these results provide a fundamental tool for the rigorous analysis of these algorithms and corresponding stochastic processes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|