# Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model

arXiv: https://arxiv.org/abs/2108.11640 · HTML: https://mlsanity.com/paper/2108.11640/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2021.

## Built on by (most cited first, 1 of 1)

- [Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images](https://mlsanity.com/paper/2202.09708/) (2022)

## Abstract (arXiv)

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.