Stereological analysis of the spatial Poisson–Voronoi tessellation
Stereological analysis of the spatial Poisson–Voronoi tessellation
复制标题
空间 Poisson-Voronoi 镶嵌的体视分析
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
U. LORZ
中科院分区：
文献类型：
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作者：
U. Hahn;U. LORZ
讨论了空间Poisson-Voronoi镶嵌的立体模型检验和参数估计器。这些测试旨在区分Poisson-Voronoi镶嵌和更规则或更不规则的镶嵌。通过仿真研究了模型检验在几种特殊的参数替代假设下的有效性。在考虑的测试中，最强大的测试是基于截面单元格面积的方差。用蒙特卡罗方法比较了空间Poisson-Voronoi镶嵌模型参数的各种体视学估计器的偏差和方差。给出了方差预测的公式。基于顶点计数的估计器是最好的。通过将估计量应用于由其他点过程模型生成的Voronoi镶嵌来研究其稳健性。
Stereological model tests and parameter estimators for the spatial Poisson–Voronoi tessellation are discussed. The tests aim to discriminate the Poisson–Voronoi tessellation from more regular or more irregular tessellations. The power of the model tests under some special parametric alternative hypotheses is investigated by simulation. Among the tests considered, the most powerful test is based on the variance of the section cell areas. Various stereological estimators for the model parameter of the spatial Poisson–Voronoi tessellation are compared with respect to their bias and variance by means of a Monte–Carlo study. Formulae are given for variance prediction. An estimator based on vertex counting is found to be the best. Robustness is investigated by applying the estimators to Voronoi tessellations generated by other point process models.