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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

Abstract

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.

Information

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

zbMATH: 1268.62005
MathSciNet: MR2409060

Digital Object Identifier: 10.1214/074921706000000563

Subjects:
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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