Statistical Inference on Spatial Random Network

空间随机网络的统计推断

• 批准号: 10680326
• 负责人: TANEMURA Masaharu
• 金额: $ 1.92万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680326/
• 关键词: Polycrystalline; Spatial Statistics; MCMC method; Bayes Procedure; Data of Point Pattern; Voronoi Polyhedra; Dynamic Algorithm; パラメトリック推定; Voronoi分割

In the field of "Spatial Statistics", the research of the parametric methods for clustered point patterns (namely, the point patterns with inhomogeneity) had been insufficient. In order to break the above status, we started to study the spatial point patterns which are assumed to be generated from the random network structures as one of the classes of inhomogeneous point patterns. Our purposes were to construct the models of spatial statistics corresponding to the above assumption, to develop a method of parametric estimating and to confirm the validity of both the model and the method. Our final object was to apply our model and method to the observed real data.As a possible parametric method, we proposed the following approach based on Bayesian procedure. Let us assume that the observed data is represendted by the configuration of points x and that the data was ocurred from the boundaries of, say, polycrystalline network in three-dimensional space. There is surely the case our assump … More tions are realistic. Let y be the unobserved generating points of the netowrk. Furthermore, we assume, on the edge of the network, the unobserved point z which has one to one correspondence to each observation x such that x=z+ε. Here we assume that ε obeys the normal distribution. Finally we suppose that the network which is generated through y is composed of Voronoi tessellation network. Under the suitable prior distributions of unobserved variables, we used Markov Chain Monte Carlo (MCMC) method for obtaining the posterior distributions.We have confirmed that our procedure is valid for the two-dimensional artificial data which was produced by computer simulation. At this stage, our results are presented at the International Conference which was held in Canada in 1999 and so on. At the same time, we prepared the publication of the FORTRAN programs wich were devised for the dynamic construction of Voronoi tessellation in two dimensions.Certain results are already published and some results are under the preparation for publication. Less

在“空间统计”领域，对聚集点模式(即具有非均质性的点模式)的参数方法研究一直不够充分。为了打破上述现状，我们开始研究由随机网络结构产生的空间点模式，它是一类非均匀的点模式。我们的目的是构建与上述假设相对应的空间统计模型，发展一种参数估计方法，并验证模型和方法的有效性。我们的最终目标是将我们的模型和方法应用于观测到的真实数据。作为一种可能的参数方法，我们提出了以下基于贝叶斯过程的方法。让我们假设观察到的数据由点x的构型表示，并且数据是从三维空间中的多晶网络的边界上出现的。我们的AsSump…肯定有这样的情况更多的选择是现实的。设y是网络的未观测产生点。此外，我们假设，在网络的边缘上，未观察点z与每个观察点x一一对应，使得x=z+ε。这里我们假设ε服从正态分布。最后，我们假设通过y生成的网络是由Voronoi细分网络组成的。在未知变量的先验分布合适的情况下，利用马尔可夫链蒙特卡罗(MCMC)方法得到后验分布，验证了该方法对计算机模拟产生的二维人工数据的有效性。在这个阶段，我们的成果将在1999年在加拿大举行的国际会议等会议上公布。同时，我们编制了FORTRAN程序的出版，这些程序是为动态构造二维Voronoi镶嵌而设计的，一些结果已经出版，一些结果正在准备出版中。较少

项目成果

種村正美: "ランダム配置に対するボロノイ領域の統計分布"形の科学会誌. 15-2. 116-117 (2000)

Masami Tanemura：“随机放置的 Voronoi 区域的统计分布”，日本科学学会杂志 15-2（2000 年）。

種村正美: "MCMC法によるランダムネットワークのベイズ推論"科学研究費シンボジウム「事前情報をもつ統計モデルの解析のための基礎理論とその応用」予稿集. 35-39 (1998)

Masami Tanemura：“使用 MCMC 方法进行随机网络的贝叶斯推理”科学研究资助研讨会论文集“利用先验信息分析统计模型的基本理论及其应用”35-39（1998）。

種村正美: "ランダム配置に対するボロノイ領域の統計分布"形の科学会誌. 15. 116-117 (2000)

Masami Tanemura：“随机放置的 Voronoi 区域的统计分布”日本科学学会杂志 15. 116-117 (2000)。

M.Tanemura: "Random tessellation network and some inference problems."Advances in Applied Probadility (SGSA). 30. 291-292 (1998)

M.Tanemura：“随机曲面细分网络和一些推理问题。”应用概率进展（SGSA）。

M.Tanemura: "Statistical inference on random tessellation network."Abstracts of 10th International Conference and Workshop on Stochastic Geometry, Stereology and …. 28-28 (1999)

M.Tanemura：“随机镶嵌网络的统计推断。”第十届随机几何、体视学和……国际会议和研讨会摘要。