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Title: Optimal thinning of MCMC output Authors:  Marina Riabiz - King's College London (United Kingdom) [presenting]
Wilson Ye Chen - University of Technology Sydney (Australia)
Jon Cockayne - University of Warwick (United Kingdom)
Pawel Swietach - Oxford University (United Kingdom)
Steven Niederer - King's College London (United Kingdom)
Chris Oates - Newcastle University (United Kingdom)
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. 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 an 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 at