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A Bayesian approach to informing decision makers: Comparisons to minimizing relative entropy
The Ninth Workshop on Information Theoretic Methods in Science and Engineering
19 September 2016
David Bickel University of Ottawa
• posterior odds = Bayes factor ⨉ prior odds
• Bayes factor = strength of evidence
Decision-maker’s loss function
Scientist’s regret function
Scientist’s odds to report
Known cost ratio
Unknown cost ratio
• Scale & reciprocal invariance ⇒ Benford’s law
Why log odds?
Geometric mean odds
Geometric mean Bayes factor
Minimax evidential distance or minimax redundancy?
Minimum evidential distance or maximum entropy?
Funded by the Natural Sciences and Engineering Research Council of Canada
Preprint coming soon … davidbickel.com "Reporting Bayes factors or probabilities to decision makers of unknown loss functions"