标题： 一种新的Ewens-Pitman分区结构表示及其通过Riordan数组和的特征化 显示英文标题

标题： A New Representation of Ewens-Pitman's Partition Structure and Its Characterization via Riordan Array Sums

摘要： 埃文斯-皮特曼的划分结构源于由Pitman-Yor过程诱导的集划分上的一致样本概率分布系统。 它在统计应用中被广泛使用，特别是在贝叶斯非参数方法中的物种抽样模型。 从无限对称群表示论的研究领域汲取灵感，我们将埃文斯-皮特曼的划分结构视为分支图上一个非极端调和函数的例子，具体来说，就是Kingman图。 采取这种观点使我们能够利用Borodin和Olshanski（《电子组合期刊》，7，2000年）提出的插值多项式方法，对该分布进行组合和代数构造。 我们用基于谢弗多项式序列的现代幽影插值方法，提供了一个埃文斯-皮特曼划分结构的新显式表示。 此外，我们证明了该分布的某些边缘可以通过Riordan数组的加权行和来计算。 通过这种方式，我们展示了可以从埃文斯-皮特曼划分结构中获得的一些总结性统计数据和估计量，可以使用生成函数的方法得到。 这种方法简化了这些通常涉及各种特殊组合函数的繁琐计算。 此外，它还具有易于符号计算的优点。 显示英文摘要

摘要： Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling models in Bayesian nonparametrics. Drawing references from the area of representation theory of the infinite symmetric group, we view Ewens-Pitman's partition structure as an example of a non-extreme harmonic function on a branching graph, specifically, the Kingman graph. Taking this perspective enables us to obtain combinatorial and algebraic constructions of this distribution using the interpolation polynomial approach proposed by Borodin and Olshanski (The Electronic Journal of Combinatorics, 7, 2000). We provide a new explicit representation of Ewens-Pitman's partition structure using modern umbral interpolation based on Sheffer polynomial sequences. In addition, we show that a certain type of marginals of this distribution can be computed using weighted row sums of a Riordan array. In this way, we show that some summary statistics and estimators derived from Ewens-Pitman's partition structure can be obtained using methods of generating functions. This approach simplifies otherwise cumbersome calculations of these quantities often involving various special combinatorial functions. In addition, it has the added benefit of being amenable to symbolic computation.