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Activity Number: 81
Type: Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #305800
Title: How Dependent Are Parameters Under Your Prior and Posterior?
Author(s): Ehsan Soofi*+ and Nader Ebrahimi and Nima Y Jalali
Companies: University of Wisconsin-Milwaukee and Northern Illinois University and University of Wisconsin-Milwaukee
Address: PO Box 742, Milwaukee, WI, 53201, United States
Keywords: Bayes' factor ; elliptical distributions ; entropy ; mutual information ; sharp hypothesis ; utility
Abstract:

Dependence of multivariate normal priors and posteriors can easily be assessed through the correlation matrices. But in general, dependence is more complicated than that could be measured by the traditional indices which fail even for the elliptical families. The mutual information measures departure of a joint distribution from independence. This measure, used in the Bayesian statistics as the expected utility of the sample (Lindley's information), provides a robust dependence index which extends the interpretations of the normal squared correlation to all distributions that are absolutely continuous relative to the product of their marginals. However, it is not applicable to singular distributions encountered in testing the sharp hypothesis of equality of two parameters. We present a modified index for singular distributions which combines the probability of the sharp hypothesis (singularity) and the mutual information index of the absolutely continuous distribution under the hypothesis of the inequality of the parameters. The posterior modified index includes the prior probability of the sharp hypothesis and the Bayes factor. Several illustrative examples will be presented.


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