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MIA Talks

Primer: Optimal thinning of mcmc output with application to cardiac electrophysiology

June 2, 2021
King's College London

Calcium is the end-point intracellular signal driving cardiac myocyte contraction, and its dynamics is described through a set of coupled ordinary differential equations (ODEs) [4]. Markov Chain Monte Carlo (MCMC) can be used to characterize the posterior distribution of the parameters of the cardiac ODEs, that can then serve as experimental design for multi-physics and multi-scale models of the whole hearth. However, MCMC suffers from poor mixing caused by the high-dimensional nature of the parameter vector and the correlation of its components, so that post-processing of the MCMC output is required. 

The use of existing 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 [2], whilst the remainder of the chain is “thinned” if compression is also required. In this talk 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 [5, 3, 1], 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 we demonstrate its effectiveness in the cardiac electrophysiology problem at hand. Software is available at http://stein-thinning.org/.