Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses

Research output: Contribution to journalArticleScientificpeer-review

Abstract

A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes factors work as an “Ockham’s razor” when testing inequality constrained hypotheses, which is not the case for the fractional Bayes factor. Two different types of prior adjusted default Bayes factors are considered. In the first type, the updated prior is based on imaginary training data. Analytical and numerical examples show that this criterion converges fastest to a true inequality constrained hypothesis. In the second type, the updated prior is based on empirical training data. This second criterion only outperforms the fractional Bayes factor in the case of small samples.
Keywords: Fractional Bayes factor, Ockham’s razor, (In)equality constraints, Updated prior
Original languageEnglish
Pages (from-to)448-463
JournalComputational Statistics and Data Analysis
Volume71
DOIs
Publication statusPublished - 2014

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Fractional Bayes Factor
Bayes Factor
Equality
Testing
Equality Constraints
Multiple Hypothesis Testing
Inequality Constraints
Small Sample
Parameter Space
Converge
Numerical Examples

Cite this

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title = "Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses",
abstract = "A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes factors work as an “Ockham’s razor” when testing inequality constrained hypotheses, which is not the case for the fractional Bayes factor. Two different types of prior adjusted default Bayes factors are considered. In the first type, the updated prior is based on imaginary training data. Analytical and numerical examples show that this criterion converges fastest to a true inequality constrained hypothesis. In the second type, the updated prior is based on empirical training data. This second criterion only outperforms the fractional Bayes factor in the case of small samples.Keywords: Fractional Bayes factor, Ockham’s razor, (In)equality constraints, Updated prior",
author = "J. Mulder",
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Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses. / Mulder, J.

In: Computational Statistics and Data Analysis, Vol. 71, 2014, p. 448-463.

Research output: Contribution to journalArticleScientificpeer-review

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