TY  - JOUR
A1  - Nüsken, Nikolas
A1  - Pavhotis, Grigorios A.
T1  - Constructing Sampling Schemes via Coupling
T2  - SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association
N2  - 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.
KW  - sampling
KW  - optimal transport
KW  - particle methods
KW  - Markov semigroups
KW  - MCMC
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/50733
SN  - 2166-2525
VL  - 7
IS  - 1
SP  - 324
EP  - 382
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -