# Topological model selection: a case-study in tumour-induced angiogenesis

## TL;DR

This paper introduces a new method combining Bayesian computation and topological analysis to compare and calibrate models of tumor-induced blood vessel growth.

## Contribution

A flexible pipeline for model selection and parameter inference using topological summary statistics in spatio-temporal models.

## Key findings

- The pipeline successfully infers four parameters in three angiogenesis models.
- The correct model is identified in synthetic test cases using topological data analysis.
- The method is validated through simulation and comparison with established models.

## Abstract

Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data. Approximate Bayesian Computation is a widely used method for parameter inference and model selection in such scenarios, and it may be combined with Topological Data Analysis to study models which simulate data with fine spatial structure.

We develop a flexible pipeline for parameter inference and model selection in spatio-temporal models. Our pipeline identifies topological summary statistics which quantify spatio-temporal data and uses them to approximate parameter and model posterior distributions. We validate our pipeline on models of tumour-induced angiogenesis, inferring four parameters in three established models and identifying the correct model in synthetic test-cases.

Simulation code for all models, data analyses, parameter inference and model selection is available online at https://github.com/rmcdomaths/tms/ and archived at https://doi.org/10.5281/zenodo.17392787.