A comparison of nonlinear population Monte Carlo and particle Markov chain Monte Carlo algorithms for Bayesian inference in stochastic kinetic models

Documento depositado en el repositorio arXiv.org. Versión: arXiv:1404.5218v1 [stat.ME]In this paper we address the problem of Monte Carlo approximation of posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in biochemical systems according to a set of uncertain parameters. Markov chain Monte Carlo (MCMC) methods have been typically preferred for this Bayesian inference problem. Specifically, the particle MCMC (pMCMC) method has been recently shown to be an effective, while computationally demanding, method applicable to this problem. Within the pMCMC framework, importance sampling (IS) has been used only as the basis of the sequential Monte Carlo (SMC) approximation of the acceptance ratio in the Metropolis-Hastings kernel. However, the recently proposed nonlinear population Monte Carlo (NPMC) algorithm, based on an iterative IS scheme, has also been shown to be effective as a Bayesian inference tool for low dimensional (predator-prey) SKMs. In this paper, we provide an extensive performance comparison of pMCMC versus NPMC, when applied to the challenging prokaryotic autoregulatory network. We show how the NPMC method can greatly outperform the pMCMC algorithm in this scenario, with an overall moderate computational effort. We complement the numerical comparison of the two techniques with an asymptotic convergence analysis of the nonlinear IS scheme at the core of the proposed method when the importance weights can only be computed approximatelyE. K. acknowledges the support of Ministerio de Educacióon of Spain ( Programa de Formación de Profesorado Universitario , ref. AP2008-00469). This work has been partially supported by Ministerio de Economía y Competitividad of Spain (program Consolider-Ingenio 2010 CSD2008-00010 COMONSENS and project COMPREHENSION TEC2012-38883-C02-01)