The Annals of Statistics

Belief Transforms and the Comparison of Hypotheses

Michael Goldstein

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Abstract

We describe a general approach to the comparison of two stochastic specifications over a collection of random quantities and then extend the comparison to collections of stochastic specifications. This comparison derives from the eigenstructure of the belief transform, which we construct in full generality for partially specified belief structures. We describe an application of the methodology, namely the comparison of hypotheses. Given various competing probabilistic specifications for a collection of observable quantities, we use the belief transform to separate those quantities for which the different models make very different predictions (and therefore which may be used to distinguish between the models) from those quantities for which the different models make similar predictions (and therefore which may be used to assess the suitability of the general class of models under consideration). Finally, we describe a particular application of hypothesis comparison which relates to the modelling of a collection of time series derived from an aluminum smelting process.

Article information

Source
Ann. Statist., Volume 19, Number 4 (1991), 2067-2089.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348386

Digital Object Identifier
doi:10.1214/aos/1176348386

Mathematical Reviews number (MathSciNet)
MR1135164

Zentralblatt MATH identifier
0755.62008

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 62G10: Hypothesis testing

Keywords
Autocorrelated errors mean comparisons partial specification prevision trend test

Citation

Goldstein, Michael. Belief Transforms and the Comparison of Hypotheses. Ann. Statist. 19 (1991), no. 4, 2067--2089. doi:10.1214/aos/1176348386. https://projecteuclid.org/euclid.aos/1176348386


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