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On a theorem of Stein relating Bayesian and classical inferences in group models
Author(s) -
Chang Ted,
Villegas Cesareo
Publication year - 1986
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315186
Subject(s) - sample space , mathematics , group (periodic table) , bayesian probability , multivariate statistics , invariant (physics) , prior probability , confidence interval , posterior probability , bayes' theorem , sample (material) , bayesian inference , mathematical economics , statistics , pure mathematics , combinatorics , physics , mathematical physics , quantum mechanics , thermodynamics
Let a group G act on the sample space. This paper gives another proof of a theorem of Stein relating a group invariant family of posterior Bayesian probability regions to classical confidence regions when an appropriate prior is used. The example of the central multivariate normal distribution is discussed.