Testing goodness of fit for point processes via topological data analysis

Christophe A. N. Biscio*, Nicolas Chenavier, Christian Hirsch, Anne Marie Svane

*Bijbehorende auteur voor dit werk

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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 correlations.

Originele taal-2English
Pagina's (van-tot)1024-1074
Aantal pagina's51
TijdschriftElectronic journal of statistics
Volume14
Nummer van het tijdschrift1
DOI's
StatusPublished - 2020

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