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Activity Number:
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535
- The American Statistician
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Type:
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Invited
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Date/Time:
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Thursday, August 6, 2020 : 1:00 PM to 2:50 PM
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Sponsor:
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The American Statistician
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Abstract #309246
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Title:
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Comparing Objective and Subjective Bayes Factors for the Two-Sample Comparison: The Classification Theorem in Action
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Author(s):
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Yonggang Lu* and Peter Westfall and Mithat Gönen and Wesley Johnson
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Companies:
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Graduate School of Business, Maine Business School, University of Maine and Texas Tech University and Memorial Sloan?Kettering Cancer Center and University of California Irvine
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Keywords:
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Decision theory;
Effect size;
Optimal classification;
Prior probability
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Abstract:
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Many Bayes factors (BFs) have been proposed for comparing population means in two-sample studies. These BFs can be categorized as “objective” or “subjective” depending on the assumed prior for the effect size parameter. A subjective prior might be formulated based on some priorly acquired scientific knowledge. An objective prior instead is selected so that the posterior has desired mathematical properties. Choosing between the two priors begs the often-debated question, “Should priors be chosen for convenience or to reflect prior knowledge?” This article discusses desiderata of BFs that have been proposed and proposes a new criterion to compare BFs that is based on a famous result in classification theory to minimize the total misclassification rate. The criterion is popular in data science circles but not well recognized in the statistics community. We show this criterion reveals clearly the effects of assuming particular priors, and thus provides new insights into the appropriateness of different BFs in general. In a broader sense, our study is calling for a thoughtful consideration of the role that prior distributions play in every empirical Bayesian data analysis.
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Authors who are presenting talks have a * after their name.
