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December, 1988 Mixtures of Distributions: A Topological Approach
L. A. Li, N. Sedransk
Ann. Statist. 16(4): 1623-1634 (December, 1988). DOI: 10.1214/aos/1176351057

Abstract

Identifiability problems have previously precluded a general approach to testing the hypothesis of a "pure" distribution against the alternative of a mixture of distributions. Three types of identifiability are defined, and it is shown that $B$-identifiability allows a Bayesian solution to the testing problem. First, an equivalence relation is defined over parametrizations of probability functions. Then the projection onto the quotient space is shown to give a $B$-identifiable parametrization. Bayesian inference proceeds using the Bayes factor as a "test" criterion.

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L. A. Li. N. Sedransk. "Mixtures of Distributions: A Topological Approach." Ann. Statist. 16 (4) 1623 - 1634, December, 1988. https://doi.org/10.1214/aos/1176351057

Information

Published: December, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0663.62021
MathSciNet: MR964942
Digital Object Identifier: 10.1214/aos/1176351057

Subjects:
Primary: 62E10
Secondary: 62F03, 62F15

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 4 • December, 1988
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