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

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.