Optimal thinning of MCMC output

Marina Riabiz; Wilson Ye Chen; Jon  Cockayne; Pawel  Swietach; Steven Niederer; Lester  Mackey; Chris Oates

Optimal thinning of MCMC output

Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven Niederer, Lester Mackey, Chris Oates^*

^*Corresponding author for this work

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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 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.

Original language	English
Journal	Journal of the Royal Statistical Society. Series B: Statistical Methodology
Publication status	Accepted/In press - 11 Jul 2021

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Optimal Thinning of MCMC Output_RIABIZ_Accepted2021_GREEN AAMAccepted author manuscript, 4.95 MB

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title = "Optimal thinning of MCMC output",

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 thatare produced. Typically a number of the initial states are attributed to “burn in” andremoved, 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 bytheir empirical distribution is close to optimal. A novel method is proposed, based ongreedy minimisation of a kernel Stein discrepancy, that is suitable when the gradientof 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.",

author = "Marina Riabiz and Chen, {Wilson Ye} and Jon Cockayne and Pawel Swietach and Steven Niederer and Lester Mackey and Chris Oates",

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T1 - Optimal thinning of MCMC output

AU - Riabiz, Marina

AU - Chen, Wilson Ye

AU - Cockayne, Jon

AU - Swietach, Pawel

AU - Niederer, Steven

AU - Mackey, Lester

AU - Oates, Chris

PY - 2021/7/11

Y1 - 2021/7/11

N2 - 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 thatare produced. Typically a number of the initial states are attributed to “burn in” andremoved, 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 bytheir empirical distribution is close to optimal. A novel method is proposed, based ongreedy minimisation of a kernel Stein discrepancy, that is suitable when the gradientof 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.

AB - 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 thatare produced. Typically a number of the initial states are attributed to “burn in” andremoved, 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 bytheir empirical distribution is close to optimal. A novel method is proposed, based ongreedy minimisation of a kernel Stein discrepancy, that is suitable when the gradientof 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.

M3 - Article

SN - 1369-7412

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

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

ER -

Optimal thinning of MCMC output

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