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In this paper we address the problem of Monte Carlo approximation ofposterior probability distributions in stochastic kinetic models (SKMs). SKMsare multivariate Markov jump processes that model the interactions amongspecies in biochemical systems according to a set of uncertain parameters.Markov chain Monte Carlo (MCMC) methods have been typically preferred for thisBayesian inference problem. Specifically, the particle MCMC (pMCMC) method hasbeen recently shown to be an effective, while computationally demanding, methodapplicable 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 effectiveas a Bayesian inference tool for low dimensional (predator-prey) SKMs. In thispaper, we provide an extensive performance comparison of pMCMC versus NPMC,when applied to the challenging prokaryotic autoregulatory network. We show howthe NPMC method can greatly outperform the pMCMC algorithm in this scenario,with an overall moderate computational effort. We complement the numericalcomparison of the two techniques with an asymptotic convergence analysis of thenonlinear IS scheme at the core of the proposed method when the importanceweights can only be computed approximately.

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