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Topology-based goodness-of-fit tests for sliced spatial data

Cipriani, Alessandra; Hirsch, Christian; Vittorietti, Martina; (2022) Topology-based goodness-of-fit tests for sliced spatial data. Computational Statistics & Data Analysis , Article 107655. 10.1016/j.csda.2022.107655. Green open access

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Abstract

In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the testing methodology through a detailed simulation study and provide a prototypical example from materials science.

Type: Article
Title: Topology-based goodness-of-fit tests for sliced spatial data
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.csda.2022.107655
Publisher version: https://doi.org/10.1016/j.csda.2022.107655
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
Keywords: Topological data analysis, Persistence diagram, Materials science, Vineyards, Goodness-of-fit tests, Asymptotic normality
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10159804
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