Optimal thinning of MCMC output
Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Lester Mackey, Chris. J. Oates
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2022 · Volume 84 · Issue 4
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, 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 theStein Thinningpackage inPython,RandMATLAB.
Keywords
Bayesian computation, greedy optimisation, Markov chain Monte Carlo, reproducing kernel, Stein's method
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