Cox process representation and inference for stochastic reaction-diffusion processes

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. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction diffusion process to data. Our solution relies on a novel, non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. We develop an efficient and flexible algorithm which shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. By using ideas from multiple disciplines, our approach provides both new and fundamental insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.