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Random partition of a finite set and related fields

有限集和相关域的随机划分

基本信息

批准号：
08680333
负责人：
SIBUYA Masaaki
金额：
$ 1.54万
依托单位：
Takachiho University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680333/
关键词：
clustering process distance between partitions frequency of frequencies number of new records size index Stirling-Carlitz polynomial Stirling number of the first kind the most random partition Ewens 確率分布 Stirling-Carlity多項式スターリング確率分布族

项目摘要

Random partition appears in the diversity of population in ecology, vocabulary of a group in linguistics, inelastic collision of particles in dynamics etc. and relates to Ziph's law in social groups. It has been advanced recently in population genetics in relation with random occurrence of new alleles.In this projects, statistical problems in the application of the model and related problems are studied. A central question is the notion of the most random partition of a finite set. This notion can be applied to the clustering technique in multivariate data analysis. Any method can be justified only if it classifies meaningful data in a systematic way, not random. A definition is proposed and characterized in some ways. Other topics :Prediction of the number of future new records. The earthquakes are well recorded, and people want safety against the strongest earthquake ever experienced. The problem is how often the record value will be broken. By new records the events are partitioned into intervals and a model of new records is developed for the prediction.A distance between partitions of a finite set can be defined similarly to Hamming distance between binary codes. The distance between independent two random partitions can be used to characterize the random partition. Moreover the distance can be used to define a center of the random partitions. Hence a sampling distributions of the random partition can be constructed.

随机划分体现在生态学中的种群多样性、语言学中的群体词汇、动力学中的粒子非弹性碰撞等方面，并与社会群体中的齐夫定律有关。最近在种群遗传学中提出了与新等位基因随机出现有关的问题。在本项目中，研究了该模型应用中的统计问题和相关问题。一个核心问题是有限集的最随机划分的概念。这一概念可应用于多元数据分析中的聚类技术。任何方法只有在以系统的方式、而不是随机的方式对有意义的数据进行分类时，才能被证明是正当的。提出了一种定义，并对其进行了刻画。其他主题：预测未来新记录的数量。地震被很好地记录下来，人们希望在经历过的最强地震中保持安全。问题是，破纪录的频率有多高。通过新记录将事件划分为区间，并建立新记录的预测模型。有限集的分区之间的距离可以类似于二进制码之间的汉明距离来定义。独立的两个随机划分之间的距离可以用来刻画随机划分。此外，距离还可以用来定义随机分区的中心。因此，可以构造随机分区的抽样分布。