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

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...

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Autores principales:	Federico Camerlenghi, Stefano Favaro
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Bayesian nonparametrics exchangeability feature-sampling model de Finetti theorem Johnson’s “sufficientness” postulate predictive distribution Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/afd2be041ecf41669e6c2c2c3cdce1ba
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id	oai:doaj.org-article:afd2be041ecf41669e6c2c2c3cdce1ba
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spelling	oai:doaj.org-article:afd2be041ecf41669e6c2c2c3cdce1ba2021-11-25T18:16:55ZOn Johnson’s “Sufficientness” Postulates for Feature-Sampling Models10.3390/math92228912227-7390https://doaj.org/article/afd2be041ecf41669e6c2c2c3cdce1ba2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2891https://doaj.org/toc/2227-7390In 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.Federico CamerlenghiStefano FavaroMDPI AGarticleBayesian nonparametricsexchangeabilityfeature-sampling modelde Finetti theoremJohnson’s “sufficientness” postulatepredictive distributionMathematicsQA1-939ENMathematics, Vol 9, Iss 2891, p 2891 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian nonparametrics exchangeability feature-sampling model de Finetti theorem Johnson’s “sufficientness” postulate predictive distribution Mathematics QA1-939
spellingShingle	Bayesian nonparametrics exchangeability feature-sampling model de Finetti theorem Johnson’s “sufficientness” postulate predictive distribution Mathematics QA1-939 Federico Camerlenghi Stefano Favaro On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
description	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.
format	article
author	Federico Camerlenghi Stefano Favaro
author_facet	Federico Camerlenghi Stefano Favaro
author_sort	Federico Camerlenghi
title	On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
title_short	On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
title_full	On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
title_fullStr	On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
title_full_unstemmed	On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models
title_sort	on johnson’s “sufficientness” postulates for feature-sampling models
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/afd2be041ecf41669e6c2c2c3cdce1ba
work_keys_str_mv	AT federicocamerlenghi onjohnsonssufficientnesspostulatesforfeaturesamplingmodels AT stefanofavaro onjohnsonssufficientnesspostulatesforfeaturesamplingmodels
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On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

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