Optimal thinning of MCMC output
Optimal thinning of MCMC output
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, whilst 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 for problems where heavy compression 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.
Riabiz, Marina
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Chen, Wilson
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Cockayne, Jonathan
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Swietach, Pawel
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Niederer, Steven A.
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Oates, Chris J.
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Riabiz, Marina
1ecee25d-b4c9-40ae-b904-819e9410a165
Chen, Wilson
14babbf3-cf1f-46ea-8401-e4455751ecdd
Cockayne, Jonathan
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Swietach, Pawel
b61b2090-5af9-45a8-9c55-0e8a6cf188ac
Niederer, Steven A.
39de3d6c-0360-455d-93de-776af21ed975
Oates, Chris J.
3af13c56-dc47-4d2c-867f-e4e933e74619
Riabiz, Marina, Chen, Wilson, Cockayne, Jonathan, Swietach, Pawel, Niederer, Steven A. and Oates, Chris J.
(2020)
Optimal thinning of MCMC output.
Pre-print.
(In Press)
Abstract
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, whilst 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 for problems where heavy compression 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.
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Optimal Thinning of MCMC Output
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Accepted/In Press date: 8 May 2020
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Local EPrints ID: 451789
URI: http://eprints.soton.ac.uk/id/eprint/451789
PURE UUID: 6a4c4be6-538f-4d08-8ee4-6952c4c4ce62
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Date deposited: 27 Oct 2021 16:32
Last modified: 17 Mar 2024 04:09
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Contributors
Author:
Marina Riabiz
Author:
Wilson Chen
Author:
Pawel Swietach
Author:
Steven A. Niederer
Author:
Chris J. Oates
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