Multiple hypothesis testing in persistent homology

We propose a general null model for persistent homology barcodes from a point cloud, to test for example acyclicity in simplicial complexes generated from point clouds. One advantage of the null model we propose is efficiency in generating a null model that applies to a broad set of hypothesis testing procedures. The second key idea in this talk is using the null model to address multiple hypothesis testing via control of family-wise error rates and false discovery rates.