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.
@article{1176351057,
author = {Li, L. A. and Sedransk, N.},
title = {Mixtures of Distributions: A Topological Approach},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 1623-1634},
language = {en},
url = {http://dml.mathdoc.fr/item/1176351057}
}
Li, L. A.; Sedransk, N. Mixtures of Distributions: A Topological Approach. Ann. Statist., Tome 16 (1988) no. 1, pp. 1623-1634. http://gdmltest.u-ga.fr/item/1176351057/