On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view
type: Item
instance of: scholarly article
title: On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view
zbMATH Open document ID: 0964.62003
DOI: 10.1016/S0167-7152(99)00089-9
author: Paloma Pérez
author: Agustín G. Nogales
author: José A. Oyola
published in: Statistics \& Probability Letters
publication date: 2001-07-19T00:00:00Z
review text: The paper presents, from a Bayesian point of view, several results about conditional independence and about its role in analyzing the relations between concepts of sufficiency and concepts of invariance. Some of the given results are, in particular, related with the Bayesian translation of the ``Stein theorem'' [see \textit{W.J. Hall}, \textit{R.A. Wijsman} and \textit{J.K. Ghosh}, Ann. Math. Stat. 36, 575-614 (1965; Zbl 0227.62007)], which gives sufficient conditions under which \({\mathcal A}_S\cap {\mathcal A}_I\) is sufficient for \({\mathcal A}_I\), where \({\mathcal A}_S\) is a sufficient \(\sigma\)-field and \({\mathcal A}_I\) is the \(\sigma\)-field of all events, invariant under the action of a given group \(G\). The paper starts with a brief review about concepts of sufficiency and invariance (both in the classic and Bayesian statistics settings) and ends with some further discussion about the Stein theorem. Some examples of the theory are provided.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62B05
zbMATH DE Number: 1395083
zbMATH Keywords: conditional independence
zbMATH Keywords: measurable space
zbMATH Keywords: sufficiency
zbMATH Keywords: invariance
Wikidata QID: Q56135048
MaRDI profile type: Publication
cites work: A Note on Sufficiency and Invariance
cites work: Q4195750
cites work: Q3996621
cites work: The Relationship Between Sufficiency and Invariance with Applications in Sequential Analysis
cites work: On sufficiency and invariance
cites work: Some remarks on sufficiency, invariance and conditional independence
full work available at URL: s0167-7152(99)00089-9
OpenAlex ID: W2014193022
description: scientific article; zbMATH DE number 1395083