Cox process representation and inference for stochastic reaction-diffusion processes

TL;DR

This paper introduces a novel method linking stochastic reaction-diffusion processes to Cox processes, enabling efficient inference and model selection for complex spatial systems in biology and epidemiology.

Contribution

It establishes a new connection between reaction-diffusion models and Cox processes, providing a practical algorithm for parameter inference and model selection.

Findings

High accuracy on biological data

Effective in epidemiological modeling

Flexible and computationally efficient

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 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 from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.