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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

  • Bayes’s theorem

    • posterior odds = Bayes factor ⨉ prior odds

    • Bayes factor = strength of evidence

  • Decision-maker’s loss function

  • Bayes action

  • 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

  • Evidential distance

  • Minimax evidential distance or minimax redundancy?

  • Minimum evidential distance or maximum entropy?

  • Finally

    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"

    http://davidbickel.com

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