Group invariant inferred distributions via noncommutative probability

Details Group invariant inferred distributions via noncommutative probability Group invariant inferred distributions via noncommutative probability

2006-11-22

arxiv.org/abs/math/0611675v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 1-19

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000563 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000563

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.

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