标题： 条件独立关系与随机排列的对数线性模型 显示英文标题

标题： Conditional independence relations and log-linear models for random permutations

摘要： 我们提出了一类新的随机排列模型，并称之为对数线性模型，这是基于用于列联表分析的对数线性模型的类比。作为特例，我们研究了所有 Luce 可分解分布的族以及那些随机排列的分布，其中排列及其逆排列的分布均为 Luce 可分解的。 我们证明这些后一类模型可以通过条件独立关系来描述。我们计算了这些模型中的自由参数数量，并描述了一个用于最大似然估计的迭代算法，这使我们可以检验一组数据是否满足条件独立关系。 显示英文摘要

摘要： We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable distributions, and the family of those random permutations, for which the distribution of both the permutation and its inverse is Luce-decomposable. We show that these latter models can be described by conditional independence relations. We calculate the number of free parameters in these models, and describe an iterative algorithm for maximum likelihood estimation, which enables us to test if a set of data satisfies the conditional independence relations or not.