Abstract

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 systems 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. In this talk, I will show how the Poisson representation of the Chemical Master Equation can be used to derive a novel connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes. This connection 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.