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Combining expert probabilities using the product of odds

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  • Patrizio Frederic
  • Mario Di Bacco
  • Frank Lad

Abstract

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert’s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios in favour of the event; that the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; that the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to the class of combining functions that honour the principles of uniformity and compromise. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Patrizio Frederic & Mario Di Bacco & Frank Lad, 2012. "Combining expert probabilities using the product of odds," Theory and Decision, Springer, vol. 73(4), pages 605-619, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:605-619
    DOI: 10.1007/s11238-012-9320-9
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    References listed on IDEAS

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    Cited by:

    1. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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