Imperial College London
Alternate

DrAndrewDuncan

Faculty of Natural Sciences, Department of Mathematics

Senior Lecturer in Statistics and Data-Centric Engineering
 
 
 
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Contact

 

a.duncan

 
 
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Location

 

6M14Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gorham:2019:10.1214/19-AAP1467,
author = {Gorham, J and Duncan, A and Vollmer, S and Mackey, L},
doi = {10.1214/19-AAP1467},
journal = {Annals of Applied Probability},
pages = {2884--2928},
title = {Measuring sample quality with diffusions},
url = {http://dx.doi.org/10.1214/19-AAP1467},
volume = {29},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Stein’s method for measuring convergence to a continuous targetdistribution relies on an operator characterizing the target andSteinfactorbounds on the solutions of an associated differential equation.While such operators and bounds are readily available for a diversityof univariate targets, few multivariate targets have been analyzed. Weintroduce a new class of characterizing operators based on Itˆo diffu-sions and develop explicit multivariate Stein factor bounds for anytarget with a fast-coupling Itˆo diffusion. As example applications, wedevelop computable and convergence-determiningdiffusion Stein dis-crepanciesfor log-concave, heavy-tailed, and multimodal targets anduse these quality measures to select the hyperparameters of biasedMarkov chain Monte Carlo (MCMC) samplers, compare random anddeterministic quadrature rules, and quantify bias-variance tradeoffsin approximate MCMC. Our results establish a near-linear relation-ship between diffusion Stein discrepancies and Wasserstein distances,improving upon past work even for strongly log-concave targets. Theexposed relationship between Stein factors and Markov process cou-pling may be of independent interest.
AU  - Gorham,J
AU  - Duncan,A
AU  - Vollmer,S
AU  - Mackey,L
DO  - 10.1214/19-AAP1467
EP  - 2928
PY  - 2019///
SN  - 1050-5164
SP  - 2884
TI  - Measuring sample quality with diffusions
T2  - Annals of Applied Probability
UR  - http://dx.doi.org/10.1214/19-AAP1467
UR  - https://projecteuclid.org/euclid.aoap/1571385625#info
UR  - http://hdl.handle.net/10044/1/68571
VL  - 29
ER  -
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