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Optimal thinning of MCMC output

Lookup NU author(s): Professor Chris Oates

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Abstract

© 2022 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to ‘burn in’ and removed, while the remainder of the chain is ‘thinned’ if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable when the gradient of the log-target can be evaluated and approximation using a small number of states is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.


Publication metadata

Author(s): Riabiz M, Chen WY, Cockayne J, Swietach P, Niederer SA, Mackey L, Oates CJ

Publication type: Article

Publication status: Published

Journal: Journal of the Royal Statistical Society. Series B: Statistical Methodology

Year: 2022

Pages: Epub ahead of print

Online publication date: 03/04/2022

Acceptance date: 11/07/2021

Date deposited: 28/04/2022

ISSN (print): 1369-7412

ISSN (electronic): 1467-9868

Publisher: John Wiley and Sons Inc.

URL: https://doi.org/10.1111/rssb.12503

DOI: 10.1111/rssb.12503


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Funding

Funder referenceFunder name
EP/P01268X/1
II-LB-1116-20001
EP/M012492/1
EP/T001569/1
FS/18/27/33543
NS/A000049/1
RG/15/9/31534
PG/15/91/31812
WT 203148/Z/16/Z
SP/18/6/33805

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