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Journal Articles Electronic Journal of Statistics Year : 2020

Testing goodness of fit for point processes via topological data analysis

Christophe Biscio
  • Function : Author
Christian Hirsch
  • Function : Author
Anne Marie Svane
  • Function : Author

Abstract

We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate functional summary statistic for observed point patterns that is asymptotically Gaussian in large observation windows. We analyze the power of tests derived from this statistic on simulated point patterns and compare its performance with global envelope tests. Finally, we apply the tests to a point pattern from an application context in neuroscience. As the main methodological contribution, we derive sufficient conditions for a functional central limit theorem on bounded persistent Betti numbers of point processes with exponential decay of correlation.

Dates and versions

hal-03611316 , version 1 (17-03-2022)

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Christophe Biscio, Nicolas Chenavier, Christian Hirsch, Anne Marie Svane. Testing goodness of fit for point processes via topological data analysis. Electronic Journal of Statistics , 2020, 14 (1), pp.1024-1074. ⟨10.1214/20-EJS1683⟩. ⟨hal-03611316⟩
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