A nonlinear population Monte Carlo scheme for Bayesian parameter estimation in a stochastic intercellular network model

We investigate the application of a novel method termed nonlinear population Monte Carlo (NPMC) to the Bayesian estimation of a subset of the static parameters of a dynamic model that captures some of the features of intercellular networks, including intercell communication. The model we propose is a continuous-time stochastic version of a coupled-repressilator system that has enjoyed popularity in the last few years. To compute the posterior probability distributions of the unknown parameters, we first convert the model into a discrete-time state-space system and then apply an NPMC algorithm, with the importance weights being approximated via particle filtering (as they are analytically intractable). We show that the resulting parameter estimates converge asymptotically in the number of Monte Carlo samples in the parameter space, even if the computational budget of the particle filters used to approximate the weights of these samples is fixed. Some illustrative numerical results are also shown.