Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. On the other hand, spatio-temporal point processes offer several computational advantages from the statistical perspective, and can be coupled to dynamics via an evolving intensity field. In this talk, I will discuss how joint time marginals of a stochastic reaction-diffusion process can be approximated in a mean-field sense by a spatio-temporal Cox process. The resulting approximation allows us to naturally define an approximate likelihood, which can be optimised with respect to the kinetic parameters of the model. We show on several examples from systems biology and epidemiology that the method yields consistently accurate parameter estimates, and can be used effectively for model selection.
Ref: Schnoerr, Grima and Sanguinetti, Nature Communications 7, 2016 also http://arxiv.org/abs/1601.01972