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首页> 外文期刊>Australian & New Zealand journal of statistics >Dependent radius marks of Laguerre tessellations: a case study
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Dependent radius marks of Laguerre tessellations: a case study

机译：Laguerre Tessellations的依赖半径痕迹：一个案例研究

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摘要

We study a particular marked three-dimensional point process sample that represents a Laguerre tessellation. It comes from a polycrystalline sample of aluminium alloy material. The 'points' are the cell generators while the 'marks' are radius marks that control the size and shape of the tessellation cells. Our statistical mark correlation analyses show that the marks of the sample are in clear and plausible spatial correlation: the marks of generators close together tend to be small and similar and the form of the correlation functions does not justify geostatistical marking. We show that a simplified modelling of tessellations by Laguerre tessellations with independent radius marks may lead to wrong results. When we started from the aluminium alloy data and generated random marks by random permutation we obtained tessellations with characteristics quite different from the original ones. We observed similar behaviour for simulated Laguerre tessellations. This fact, which seems to be natural for the given data type, makes fitting of models to empirical Laguerre tessellations quite difficult: the generator points and radius marks have to be modelled simultaneously. This may imply that the reconstruction methods are more efficient than point-process modelling if only samples of similar Laguerre tessellations are needed. We also found that literature recipes for bandwidth choice for estimating correlation functions should be used with care.
机译：我们研究了一个特定标记的三维点过程样本，代表了一个Laguerre曲面细分。它来自铝合金材料的多晶样品。 “点”是小区生成器，而“标记”是控制曲面细胞的大小和形状的半径标记。我们的统计标记相关性分析表明，样品的标记处于明显和合理的空间相关性：发电机的刻度倾向于很小，类似，相关函数的形式并不合理地证明地质统计标记。我们表明，Laguerre Telsellations具有独立半径标记的简化建模可能导致错误的结果。当我们从铝合金数据开始并通过随机排列产生随机标记时，我们获得了与原始的特征不同的曲面。我们观察了模拟Laguerre Tessellations的类似行为。这一事实似乎是对给定数据类型的自然，使模型的拟合是经验的laguerre曲面图相当困难：发电机点和半径标记必须同时建模。这可能意味着如果只需要类似的LAGUERRE TESSELLATION的样本，重建方法比点流程建模更有效。我们还发现，应小心使用用于估计相关函数的带宽选择的文献食谱。

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