种群抽样模型预测概率函数的定义
Defining Predictive Probability Functions for Species Sampling Models
摘要：
我们回顾了物种抽样模型（SSM）类。特别地，我们研究了可交换分区概率函数（EPPF）和预测概率函数（PPF）之间的关系。从EPPF定义PPF很简单，但反过来不一定正确。在本文中，我们介绍了假定的PPF的概念，并显示新的条件，一个假定的PPF定义一个EPPF。我们表明，在一定的类中的所有可能的PPF必须定义（非归一化）概率的集群成员是线性的集群大小。给出了任意假定PPF定义EPPF的一个新的充分必要条件。最后，我们展示了一个大类的SSM与PPF的后验推断，这不是线性的集群大小，并讨论了数值方法来推导其PPF。
英文摘要：
We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized) probabilities for cluster membership that are linear in cluster size. We give a new necessary and sufficient condition for arbitrary putative PPFs to define an EPPF. Finally, we show posterior inference for a large class of SSMs with a PPF that is not linear in cluster size and discuss a numerical method to derive its PPF.
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