In the 1920's, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson's "sufficientness" postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e. species-sampling models. In this paper, we review "sufficientness" postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general features-sampling models. In particular, we present a "sufficientness" postulate for a class of features-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of features-sampling models.
翻译:在1920年代,英国哲学家W.E. Johnson从预测分布的角度介绍了对称 Dirichlet先前分布特征的定性,通常称之为Johnson的“适足性”假设,这是巴伊西亚统计中许多贡献的主题,导致对Drichlet分布的无穷多维概括化的预测性定性,即物种抽样模型。在本文中,我们审查了物种抽样模型的“适足性”假设,然后调查了更一般性特征抽样模型的类似预测性定性。特别是,我们为被称为“规模进程”的一组特征抽样模型提出了“适足性”假设,然后讨论了特征抽样模型总体设置中的类似特征定性。