We demonstrate the superiority of Population Monte Carlo techniques over standard Metropolis Markov Chain Monte Carlo (MCMC) methods for inferring optimal parameters for a particular mechanistic model of a biological process given noisy experimental data. As our understanding of biological processes increases, the proposed models to describe them become more complex. With such potentially large numbers of equations and parameters, it is no longer feasible to hand-pick parameter values and be sure that the most appropriate values have been chosen. Monte Carlo methods are becoming more widely used for estimating parameter values, however we show that the standard Metropolis MCMC approach fails to converge on optimal values for even relatively simple models and that a more sophisticated method, in the form of non-Markovian Population Monte Carlo, may be successfully employed to produce consistent and accurate results. We illustrate the basic problem using the minimal model for the circadian genetic network in Arabidopsis thaliana, which consists of 3 linked differential equations containing a total of 6 parameters, with an additional noise parameter incorporated to estimate the variance of noise in the data.

Joint work with Mark Girolami.