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.

Camerlenghi, F., Favaro, S. (2021). On johnson’s “sufficientness” postulates for feature-sampling models. MATHEMATICS, 9(22) [10.3390/math9222891].

On johnson’s “sufficientness” postulates for feature-sampling models

Camerlenghi F.
;
2021

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.
Articolo in rivista - Articolo scientifico
Bayesian nonparametrics; De Finetti theorem; Exchangeability; Feature-sampling model; Johnson’s “sufficientness” postulate; Predictive distribution; Scaled process prior; Species-sampling model;
English
2021
9
22
2891
open
Camerlenghi, F., Favaro, S. (2021). On johnson’s “sufficientness” postulates for feature-sampling models. MATHEMATICS, 9(22) [10.3390/math9222891].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/342338
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