Statistical Inference on Interacting Particle Systems

Abstract: Interacting particle systems, and more specifically stochastic dynamical systems, is a mathematical framework which allows for condensed and elegant modelling of complex phenomena undergoing both deterministic and random dynamics. This thesis is concerned with the topic of statistical inference on large systems of interacting particles, with the specific application of in vitro migration of cancer cells. In the first of two papers appended with this thesis, we introduce a novel method of inference based on a higher order numerical approximation of the underlying stochastic differential equations. In the second paper, we formulate a model for glioblastoma cell migration, and conduct inference on this model using microscopy data. This regression shows promising results in its predictive power.