Computation Reuse in MCMC Modelling of Ion Channel Records

J.A. Stark, W.J. Fitzgerald and S.B.Hladky

Sixth Valencia International Meeting on Bayesian Statistics, June 1998

In many applications of Markov chain Monte Carlo (MCMC) some moves can be proposed using the Gibbs paradigm, but larger moves which use the Metropolis-Hastings (M-H) paradigm are desirable in order to speed exploration of the parameter space. We discuss a framework for combining moves so that the computations required to propose and evaluate M-H-type moves can be recycled in a secondary move. This is applied to the MCMC analysis of patch-clamp records with small numbers of channels. Since there are typically more than one million data points, the efficiency of the sampler is of central importance and wastage of computation should be minimised. The aim of the research was to `idealise' the signal (rather than to fit a hidden Markov model). In the chosen model the underlying signal is piecewise constant, any conductance level is permitted and there are no long-range constraints. A multiple-order sampler was implemented in which the computation used to propose and evaluate primary moves.