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Inference on random partition models.

随机分区模型的推断。

基本信息

批准号：
06680288
负责人：
SIBUYA Masaaki
金额：
$ 1.34万
依托单位：
Keio University,
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06680288/
关键词：
urn model GEM distribution Ewens sampling formula record breaking independence test UMP test Ewens確率分布 DTG確率分布 GEM確率分布

项目摘要

A.Regard a random partition of a finite set as a process to throw balls into urns, and note that the distinguishability or undistinguishability of balls and urns are essential in the model. There are four cases by the distinction. If the random partition is consistent in these cases and for any number of balls, there are some regularity in probability laws :(1) The probability disribution depends on the number of balls in urns, but not on what balls.(2) Along with the sequence number of urns, the number of balls has a Markovian property.(3) If the number of balls is changed, the distribution of less balls is a marginal distribution of the one of more balls.These three properties are essential in fundamental random partitions. Some of the properties are enough to characterize the four kinds of families of partitions with a single positive parameter. (Japan J.Industr.Appl.Math.)B.In the ecoligical study of the variety of species, frequently used is the "residual allocation model", which … More generate the GEM distribution on the standard simplex of of the infinite dimension. The random partition of undistinguishable balls is the discrete version of the model.As the number of balls increses to infinity, the ratio of balls in urns approaches to the GEM distribution. Based on the relationship, we characterize the GEM distribution in terms of the urn model and vice versa. (Statistics and Probability Letters).C.The four kinds of families of random partitions with a parameter alpha>0 has the common minimal sufficient statistic, the number of urns occupied by balls. The number has the power series type distribution (the discrete exponential-type), and it is, when alpha=1, the distribution of the number of upper new records of any i.i.d. sequence of continuous random variables.Hence, the new-record-number test of the independence is the Uniformly Most Powerful nonparametric test against alpha>1. Its power is compared with kendall's gamma test, and it is discussed when such an alternative will appear. Tokyo monthly average temperature, in August in the past 45 years, is significant by our test, but not so by gamma test.(Japan.J.Applied Statistics.). Less

A.将有限集的随机划分视为将球扔进瓮的过程，并注意球和瓮的可区分性或不可区分性在模型中至关重要。按情况区分有四种情况。如果在这些情况下并且对于任意数量的球，随机划分是一致的，则概率定律存在一些规律性：（1）概率分布取决于瓮中球的数量，而不取决于球的数量。（2）随着瓮的序列号，球的数量具有马尔可夫性质。（3）如果球的数量改变，则较少球的分布是较多球之一的边际分布。这些三个属性对于基本随机分区至关重要。其中一些属性足以用单个正参数来表征四种分区族。 (Japan J.Industr.Appl.Math.)B.在物种多样性的生态研究中，经常使用的是“剩余分配模型”，它在无限维的标准单纯形上生成GEM分布。不可区分的球的随机划分是该模型的离散版本。随着球的数量增加到无穷大，瓮中球的比例接近GEM分布。基于这种关系，我们用 urn 模型来表征 GEM 分布，反之亦然。（统计和概率字母）.C. 参数 alpha > 0 的四种随机分区族具有共同的最小充分统计量，即球占据的瓮的数量。该数具有幂级数型分布（离散指数型），是当 alpha=1 时，任意 i.i.d. 的上新记录数的分布。连续随机变量的序列。因此，独立性的新记录数检验是针对 alpha>1 的一致最有力的非参数检验。它的功效与肯德尔的伽马测试进行了比较，并讨论了何时会出现这样的替代方案。过去 45 年中东京 8 月份的月平均气温，根据我们的测试显着，但通过伽马测试则不显着。（Japan.J.Applied Statistics.）。较少的