2014/04/21 by Eugenia Koblents, Koblents, Eugenia, Joaquı́n Mı́guez +2
Mathematics · #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.1404.5218
arxiv created 2014/04/21 · openalex publication_date 2014/04/21 · arxiv updated 2014/04/22 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28
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 approximately.