On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

Federico Camerlenghi and Stefano Favaro
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Federico Camerlenghi: Department of Economics, Management and Statistics, University of Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126 Milano, Italy
Stefano Favaro: Collegio Carlo Alberto, Piazza V. Arbarello 8, 10122 Torino, Italy

Mathematics, 2021, vol. 9, issue 22, 1-15

Abstract: In the 1920s, 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 feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

Keywords: Bayesian nonparametrics; exchangeability; feature-sampling model; de Finetti theorem; Johnson’s “sufficientness” postulate; predictive distribution; scaled process prior; species-sampling model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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