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VOL. 50 | 2006 Group invariant inferred distributions via noncommutative probability
B. Heller, M. Wang

Editor(s) Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page


One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Bayes’ method and in particular without using a joint distribution of random variable and parameter. In the Poisson and binomial cases, the final formulas for inferred distributions coincide with the formulas for Bayes posteriors with uniform priors.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62005
MathSciNet: MR2409060

Digital Object Identifier: 10.1214/074921706000000563

Primary: 62A05 , 62F99
Secondary: 62A30 , 62F15

Keywords: coherent states , group representations , non-informative prior or reference prior , spectral measures , statistical inference

Rights: Copyright © 2006, Institute of Mathematical Statistics


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