Year: 2021
Type: article
Abstract: We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [2] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to equilibrium. We make use of weak Poincaré inequalities, as developed in the work of [15], the ideas of which we adapt to the PDMPs of interest. On the way we report largely potential-independent approaches to bounding explicitly solutions of the Poisson equation of the Langevin diffusion and its first and second derivatives, required here to control various terms arising in the application of the hypocoercivity result.
DOI: 10.1214/21-ejp643
Authors: Christophe Andrieu, Paul Dobson, Andi Q. Wang
Institutions: University of Bristol, Delft University of Technology
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
Awards: G1579515842, G1871434800, G1974824942, G3402893575, Zig-Zagging through Computational Barriers, New Approaches to Bayesian Data Science: Tackling Challenges from the Health Sciences, G6631254222, G8722502606, G926698369, CoSInES (COmputational Statistical INference for Engineering and Security)
OpenAlex ID: W3098860869