论文标题
基于同源性的拟合优点测试用于空间镶嵌
Persistent homology based goodness-of-fit tests for spatial tessellations
论文作者
论文摘要
由于材料科学领域的虚拟材料设计的迅速相关性的迅速相关性，它对于评估空间镶嵌的随机模型的拓扑特性是否与给定数据集相一致。最近，诸如持久图之类的拓扑数据分析的工具已允许在各种应用程序环境中获得深刻的见解。在这项工作中，我们建立了从持久图的细节改进得出的各种测试统计量的渐近正态性。由于在应用程序中，通常可以使用与交互作用的Tessellation数据一起工作，因此我们为Voronoi和Laguerre Tessellations建立了我们的主要结果，它们的发电机形成Gibbs点过程。我们阐明如何使用这些概念结果来得出拟合测试的优点，然后在模拟研究中研究其功能。最后，我们将测试方法应用于描述真实泡沫数据的细节。
Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data.
