Ergodicity of the zigzag process

By Joris Bierkens, Gareth O. Roberts, Pierre-André Zitt. The Annals of Applied Probability, 2017

80 citations recorded by the source corpus.

The zigzag process is a Piecewise Deterministic Markov Process which can be used in a MCMC framework to sample from a given target distribution. We prove the convergence of this process to its target under very weak assumptions, and establish a central limit theorem for empirical averages under stronger assumptions on the decay of the target measure. We use the classical "Meyn-Tweedie" approach. The main difficulty turns out to be the proof that the process can indeed reach all the points in the space, even if we consider the minimal switching rates.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/da0f4a15467b09277b67a26cf7a67736ec344020

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Citations in the corpus

Posterior Computation with the Gibbs Zig-Zag Sampler (2020, methodology): “If the rate functions have the form with γ i ( ζ ) ≥ 0 , this ensures that (cid:101) π is an invariant measure of the process (Bierkens et al., 2019a), where ζ = ( ζ 1 , . . . , ζ d ) .”
Efficient posterior sampling for high-dimensional imbalanced logistic regression. (2019, background): “In particular, under certain technical conditions on the potential function U , exponential convergence in the law of the zig-zag process has been shown [7, 9, 2].”
Geometric ergodicity of the Bouncy Particle Sampler (2018, result): “Contrary to the previous works [35, 10, 5], this result is obtained in the case where µ v has a density with respect to the Lebesgue measure by a direct coupling.”