Bayesian Inference for Markov Processes with Application to Biochemical Network Dynamics
Darren J. Wilkinson
School of Maths and Stats, Newcastle University, Newcastle upon Tyne, England, United Kingdom

A number of interesting statistical applications involve the estimation of parameters underlying a complex continuous time Markov process model using partial and noisy discrete time data on the time course dynamics of the system. Bayesian inference for this problem is difficult due to the fact that the discrete time transition density of the Markov process is typically intractable, and computationally intensive to approximate. In many cases it is possible to approximate either the model or the inferential algorithm in order to make progress. However it is also possible, at least in principle, to develop MCMC algorithms that are exact, provided that one can simulate exact realisations of the process forwards in time. Such algorithms, often termed “likelihood free” or “likelihood free” are very attractive, as they allow separation of the problem of model development and simulation implementation from the development of inferential algorithms. This talk will provide an overview of likelihood free approaches to parameter inference for Markov processes, and illustrate the techniques in the context of a problem in systems biology concerning the estimation of rate constants for a stochastic biochemical network model of a bacterial decision process, using single cell time course data on a fluorescent reporter protein.

Keywords: Stochastic modelling; Systems biology; Bayesian inference; Bacterial decision network

Biography: Darren Wilkinson is Professor of Stochastic Modelling at Newcastle University. He joined Newcastle University in 1996, after studying for a first degree and PhD at nearby Durham University. His background is in computational Bayesian inference, but in recent years he has become increasingly interested in applications of statistical methods to challenging problems in computational systems biology. He currently holds a BBSRC Research Development Fellowship to study noise, stochasticity and heterogeneity in model biological systems.