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We investigate a stochastic version of the synthetic multicellular clockmodel proposed by Garcia-Ojalvo, Elowitz and Strogatz. By introducing dynamicalnoise in the model and assuming that the partial observations of the system canbe contaminated by additive noise, we enable a principled mechanism torepresent experimental uncertainties in the synthesis of the multicellularsystem and pave the way for the design of probabilistic methods for theestimation of any unknowns in the model. Within this setup, we investigate theuse of an iterative importance sampling scheme, termed nonlinear populationMonte Carlo (NPMC), for the Bayesian estimation of the model parameters. Thealgorithm yields a stochastic approximation of the posterior probabilitydistribution of the unknown parameters given the available data (partial andpossibly noisy observations). We prove a new theoretical result for thisalgorithm, which indicates that the approximations converge almost surely tothe actual distributions, even when the weights in the importance samplingscheme cannot be computed exactly. We also provide a detailed numericalassessment of the stochastic multicellular model and the accuracy of theproposed NPMC algorithm, including a comparison with the popular particleMetropolis-Hastings algorithm of Andrieu {\em et al.}, 2010, applied to thesame model and an approximate Bayesian computation sequential Monte Carlomethod introduced by Mari\~no {\em et al.}, 2013.

An iterative importance sampler for Bayesian parameter estimation in stochastic models of multicellular clocks