open access publication

Article, 2023

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

In: Computational Statistics & Data Analysis, ISSN 1872-7352, 0167-9473, Volume 179, Ann. Appl. Probab. 15 2005, Page 107655, 10.1016/j.csda.2022.107655

Contributors (3)

Cipriani, Alessandra (0000-0001-9486-101X) [1] [2] Hirsch, Christian (0000-0003-4136-3740) (Corresponding author) [3] [4] Vittorietti, Martina (0000-0002-7695-3209) [5]

Affiliations

  1. [1] Department of Statistical Science, UCL, United Kingdom of Great Britain and Northern Ireland
  2. [2] University College London
  3. [NORA names: United Kingdom; Europe, Non-EU; OECD]
  4. [3] Aarhus University
  5. [NORA names: AU Aarhus University; University; Denmark; Europe, EU; Nordic; OECD]
  6. [4] University of Groningen
  7. [NORA names: Netherlands; Europe, EU; OECD]
  8. [5] University of Palermo
  9. [NORA names: Italy; Europe, EU; OECD]

Abstract

In materials science and many other application domains, 3D information can often only be obtained by extrapolating from 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. It is illustrated 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 statistics, goodness-of-fit tests that become asymptotically exact in large sampling windows are devised. The testing methodology is illustrated through a detailed simulation study and a prototypical example from materials science is provided.

Keywords

analysis, application domains, asymptotic normality, data, data analysis, detailed simulation study, domain, example, features, fit test, goodness, hypothesis test, information, materials science, methodology, microstructure model, model, normality, powerful tool, prototypical example, sampling window, science, simulation study, slices, spatial data, statistical hypothesis test, statistics, study, test, testing methodology, tool, topological data analysis, topological features, vineyards, window

Funders

  • Dutch Research Council
  • Ministry of Economic Affairs and Climate Policy