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Inferring the parameters of models describing biological systems is animportant problem in the reverse engineering of the mechanisms underlying thesesystems. Much work has focused on parameter inference of stochastic andordinary differential equation models using Approximate Bayesian Computation(ABC). While there is some recent work on inference in spatial models, thisremains an open problem. Simultaneously, advances in topological data analysis(TDA), a field of computational mathematics, have enabled spatial patterns indata to be characterised. Here we focus on recent work using topological dataanalysis to study different regimes of parameter space for a well-studied modelof angiogenesis. We propose a method for combining TDA with ABC to inferparameters in the Anderson-Chaplain model of angiogenesis. We demonstrate thatthis topological approach outperforms ABC approaches that use simplerstatistics based on spatial features of the data. This is a first step towardsa general framework of spatial parameter inference for biological systems, forwhich there may be a variety of filtrations, vectorisations, and summarystatistics to be considered. All code used to produce our results is availableas a Snakemake workflow.

Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model