Statistical inference on discrete patterns on random structures

主要研究成果如下。提出了一种求取无向图模型上观察到的离散模式个数的精确分布的方法。对于可交换或部分可交换的试验序列上观察到的离散模式，提出了参数统计模型。给出了可交换序列的混合度量。在此基础上，利用优惠券收集者的问题，提出了一个关于置换群的参数统计模型。该统计模型可用于最大似然估计和似然比检验等排序数据的统计推断。

Main results of the research are as follows. A method for deriving exact distributions of numbers of discrete patterns observed on undirected graphical models is proposed. Parametric statistical models are proposed for observed discrete patterns on exchangeable or partially exchangeable sequences of trials. The mixing measures of the exchangeable sequences also obtained. Further, a parametric statistical model on the permutation group is proposed by using the coupon collecter's problems. The statistical model is useful for statistical inference of ranking data such as maximum likelihood estimation and likelihood ratio tests.