论文标题
基于拓扑的拟合优度测试切片空间数据
Topology-based goodness-of-fit tests for sliced spatial data
论文作者
论文摘要
在材料科学和许多其他应用领域中，通常只能通过使用2D切片来推断3D信息。在拓扑数据分析中，持久性葡萄园已成为一种强大的工具，可以考虑在几个切片上延伸的拓扑特征。在本文中，我们说明了如何使用持久性葡萄园来设计基于2D切片数据的3D微观结构模型的严格统计假设测试。更确切地说，通过建立合适的纵向和横截面摘要统计的渐近正态性，我们设计了拟合优度测试，这些测试在大型采样窗口中变得渐近确切。我们通过详细的仿真研究说明了测试方法，并提供了材料科学的典型示例。
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.
