6533b85dfe1ef96bd12bddde
RESEARCH PRODUCT
Topology-based goodness-of-fit tests for sliced spatial data
Alessandra CiprianiMartina VittoriettiChristian Hirschsubject
Computational Geometry (cs.CG)FOS: Computer and information sciencesStatistics and ProbabilityGoodness-of-fit testsApplied MathematicsTopological data analysisPersistence diagramMathematics - Statistics TheoryStatistics Theory (math.ST)VineyardsMaterials scienceComputational MathematicsComputational Theory and Mathematics60F05Topological data analysis Persistence diagram Materials science Vineyards Goodness-of-fit tests Asymptotic normalityFOS: MathematicsAlgebraic Topology (math.AT)Computer Science - Computational GeometryAsymptotic normalityMathematics - Algebraic Topologydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-03-01 | Computational Statistics & Data Analysis |