Imperial College London

Professor Grigorios A. Pavliotis

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Nüsken:2019:10.1137/18m119896x,
author = {Nüsken, N and Pavliotis, GA},
doi = {10.1137/18m119896x},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
pages = {324--382},
title = {Constructing sampling schemes via coupling: Markov semigroups and optimal transport},
url = {http://dx.doi.org/10.1137/18m119896x},
volume = {7},
year = {2019}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - 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 Poincaré inequality.
AU - Nüsken,N
AU - Pavliotis,GA
DO - 10.1137/18m119896x
EP - 382
PY - 2019///
SN - 2166-2525
SP - 324
TI - Constructing sampling schemes via coupling: Markov semigroups and optimal transport
T2 - SIAM/ASA Journal on Uncertainty Quantification
UR - http://dx.doi.org/10.1137/18m119896x
UR - http://hdl.handle.net/10044/1/69635
VL - 7
ER -