Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces

@article{Blumberg2014RobustSH,
  title={Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces},
  author={Andrew J. Blumberg and Itamar Gal and Michael A. Mandell and Matthew Pancia},
  journal={Foundations of Computational Mathematics},
  year={2014},
  volume={14},
  pages={745-789}
}
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. 
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