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

Area of Science:

• Computational Biology
• Mathematical Modeling
• Statistical Inference

Background:

• Evaluating scientific theories relies on comparing mathematical models.
• Exact calibration methods fail for probabilistic models simulating high-dimensional spatio-temporal data.
• Approximate Bayesian Computation (ABC) and Topological Data Analysis (TDA) offer solutions for parameter inference and model selection in complex scenarios.

Purpose of the Study:

• Develop a flexible computational pipeline for parameter inference and model selection in spatio-temporal models.
• Integrate TDA with ABC to analyze models generating data with fine spatial structures.
• Quantify spatio-temporal data using topological summary statistics.

Main Methods:

• Developed a pipeline combining ABC and TDA for parameter inference and model selection.
• Identified topological summary statistics to characterize spatio-temporal data.
• Approximated parameter and model posterior distributions using the identified statistics.

Main Results:

• Successfully validated the pipeline on models of tumor-induced angiogenesis.
• Inferred four parameters across three established angiogenesis models.
• Correctly identified the appropriate model in synthetic test cases.

Conclusions:

• The developed pipeline provides a robust framework for analyzing complex spatio-temporal models.
• The integration of TDA with ABC enhances parameter inference and model selection capabilities.
• This approach is effective for biological modeling, specifically in angiogenesis research.