Exchangeability, Correlation, and Bayes' Effect |
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Authors: | Ben O'Neill |
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Affiliation: | School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia E-mails: , |
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Abstract: | We examine the difference between Bayesian and frequentist statistics in making statements about the relationship between observable values. We show how standard models under both paradigms can be based on an assumption of exchangeability and we derive useful covariance and correlation results for values from an exchangeable sequence. We find that such values are never negatively correlated, and are generally positively correlated under the models used in Bayesian statistics. We discuss the significance of this result as well as a phenomenon which often follows from the differing methodologies and practical applications of these paradigms – a phenomenon we call Bayes' effect. |
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Keywords: | Bayesian statistics frequentist statistics exchangeability independence correlation pseudo-correlation Bayes' effect |
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