Kernel Stein discrepancy minimization for MCMC thinning in cardiac electrophysiology

This is presented by the Bayesian Section of the Statistical Society of Australia

Guest speaker: Dr Marina Riabiz, King’s College, London

Abstract:

Calcium is the end-point intracellular signal driving cardiac myocyte contraction, and its dynamic is described through coupled ordinary differential equations (ODEs). Markov Chain Monte Carlo (MCMC) can be used to characterize the posterior distribution of the parameters of the cardiac ODEs, which can then serve as an experimental design for multi-scale models of the whole hearth. However, MCMC suffers from poor mixing in high-dimensional settings, so post-processing of the MCMC output is required. Existing heuristics to assess the convergence and compress the MCMC output can produce sub-optimal empirical approximations, that suffer from bias-variance trade-offs if the length of the MCMC output is fixed. In this talk, I will present a novel method that retrospectively selects a subset of states, of fixed cardinality, from the sample path, such that the approximation provided by their empirical distribution is close to optimal. This is based on greedy minimisation of a kernel Stein discrepancy, and it 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 I will demonstrate its effectiveness in the cardiac electrophysiology problem at hand, together with interesting biological findings.