Robust statistics, hypothesis testing, and confidence intervals for   persistent homology on metric measure spaces
  We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis. 
Andrew J. Blumberg, Itamar Gal, Michael A. Mandell, and Matthew Pancia
cs.CG