Parametric Inference using Persistence Diagrams: A Case Study in Population Genetics

TL;DR

This paper demonstrates how persistent homology can be used for parametric inference in population genetics, applying the method to influenza data to reveal biologically meaningful topological structures.

Contribution

It introduces a novel approach for statistical inference using persistence diagrams in population genetics, specifically applying it to the coalescent with recombination model.

Findings

Identified two distinct topological scales in influenza data

Demonstrated the feasibility of parametric inference with persistence diagrams

Provided biological interpretation of topological features

Abstract

Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed using statistics defined on the computed invariants. We develop this idea with a model from population genetics, the coalescent with recombination. We apply our model to an influenza dataset, identifying two scales of topological structure which have a distinct biological interpretation.