We consider a random marked tessellation in which the marks are crystal lattice orientations. A natural task is to construct a statistical test to decide whether the orientations are independently assigned to the cells of the underlying tessellation. The distribution of a given orientation is either identical for all cells or may depend on the corresponding cell. For both cases, non-parametric tests are developed. Using simulations, power computations are conducted for alternative models with different forms of mark correlation. We demonstrate the application in the analysis of polycrystalline materials with cubic symmetry of the crystal lattice.

中文翻译：

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标有晶体学取向的随机镶嵌

我们考虑其中标记是晶格取向的随机标记镶嵌。一个自然的任务是构造一个统计测试来确定方向是否独立地分配给底层镶嵌的单元。给定方向的分布对于所有单元格都是相同的，或者可能取决于相应的单元格。对于这两种情况，都开发了非参数测试。使用模拟，对具有不同形式的标记相关性的替代模型进行功效计算。我们证明了在具有晶格立方对称性的多晶材料分析中的应用。