Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model

Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focussed on parameter inference of stochastic and ordinary differential equation models using Approximate Bayesian Computation (ABC). While there is some recent work on inference in spatial models, this remains an open problem. Simultaneously, advances in topological data analysis (TDA), a field of computational mathematics, has enabled spatial patterns in data to be characterised. Here, we focus on recent work using topological data analysis to study different regimes of parameter space of a well-studied model of angiogenesis. We propose a method for combining TDA with ABC for inferring parameters in the Anderson-Chaplain model of angiogenesis. We demonstrate that this topological approach outperforms simpler statistics based on spatial features of the data. This is a first step towards a larger framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorisations, and summary statistics to be considered.