## The Annals of Statistics

### Mixtures of Distributions: A Topological Approach

#### 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.

#### Article information

Source
Ann. Statist., Volume 16, Number 4 (1988), 1623-1634.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176351057

Digital Object Identifier
doi:10.1214/aos/1176351057

Mathematical Reviews number (MathSciNet)
MR964942

Zentralblatt MATH identifier
0663.62021

JSTOR