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Persistent homology based goodness-of-fit tests for spatial tessellations


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Hirsch, Christian ; Krebs, Johannes ; Redenbach, Claudia:
Persistent homology based goodness-of-fit tests for spatial tessellations.
In: Journal of nonparametric statistics. 36 (2024) 1. - S. 39-59.
ISSN 1029-0311 ; 1048-5252


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Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data.

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Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Statistik
DOI / URN / ID:10.1080/10485252.2023.2280022
Verlag:Taylor & Francis
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Ja
Eingestellt am: 30. Apr 2024 13:39
Letzte Änderung: 30. Apr 2024 13:39
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