Constructing Sampling Schemes via Coupling
- In this paper we develop a general framework for constructing and analyzing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of interest, including the asymptotic variance, the task of finding efficient couplings can be phrased in terms of problems related to optimal transport theory. We investigate general structural properties, proving a singularity theorem that has both geometric and probabilistic interpretations. Moreover, we show that those problems can often be solved approximately and support our findings with numerical experiments. For the particular objective of estimating the variance of a Bayesian posterior, our analysis suggests using novel techniques in the spirit of antithetic variates. Addressing the convergence to equilibrium of coupled processes we furthermore derive a modified Poincare inequality.
Author details: | Nikolas NüskenORCiD, Grigorios A. PavhotisORCiD |
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DOI: | https://doi.org/10.1137/18M119896X |
ISSN: | 2166-2525 |
Title of parent work (English): | SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association |
Subtitle (English): | Markov Semigroups and Optimal Transport |
Publisher: | Society for Industrial and Applied Mathematics |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/03/26 |
Publication year: | 2019 |
Release date: | 2021/05/19 |
Tag: | MCMC; Markov semigroups; optimal transport; particle methods; sampling |
Volume: | 7 |
Issue: | 1 |
Number of pages: | 59 |
First page: | 324 |
Last Page: | 382 |
Funding institution: | EPSRC through a Roth Departmental Scholarship; EPSRCEngineering & Physical Sciences Research Council (EPSRC) [EP/P031587/1, EP/L024926/1, EP/L020564/1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |