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.
翻译:在材料科学和许多其他应用领域,三维信息往往只能通过取二维切片来推断。在地形数据分析中,持久性葡萄园已成为一种强有力的工具,可以考虑到跨越几个切片的地形特征。在本文件中,我们举例说明如何利用持久性葡萄园,根据二维切片的数据,为三维微观结构模型设计严格的统计假设测试。更准确地说,通过确定适当的纵向和跨部门摘要统计的无症状常度,我们设计出在大型采样窗口中变得无症状的完善试验。我们通过详细的模拟研究来说明试验方法,并提供材料科学的典型例子。