  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 focused 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, have 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 for a well-studied model
of angiogenesis. We propose a method for combining TDA with ABC to infer
parameters in the Anderson-Chaplain model of angiogenesis. We demonstrate that
this topological approach outperforms ABC approaches that use simpler
statistics based on spatial features of the data. This is a first step towards
a general framework of spatial parameter inference for biological systems, for
which there may be a variety of filtrations, vectorisations, and summary
statistics to be considered. All code used to produce our results is available
as a Snakemake workflow.
