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

TL;DR

This paper introduces a novel statistical testing framework using persistence vineyards from topological data analysis to assess 3D microstructure models based on 2D slice data, with proven asymptotic properties.

Contribution

It develops rigorous goodness-of-fit tests for 3D models using persistence vineyards, establishing their asymptotic normality and applicability to large samples.

Findings

Tests are asymptotically exact for large samples.

Simulation studies validate the testing methodology.

Application to materials science data demonstrates practical utility.

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.