On Johnson's "sufficientness" postulates for features-sampling models

TL;DR

This paper reviews Johnson's

Contribution

It introduces a new

Findings

Sufficientness postulate for Scaled Processes (SPs)

Predictive characterizations for features-sampling models

Extension of Johnson's postulate to more general models

Abstract

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.