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Avoiding both the Garbage-In/Garbage-Out and the Borel Paradox in updating probabilities given experimental information

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  • Robert Bordley

Abstract

Bayes Rule specifies how probabilities over parameters should be updated given any kind of information. But in some cases, the kind of information provided by both simulation and physical experiments is information on how certain output parameters may change when other input parameters are changed. There are three different approaches to this problem, one of which leads to the Garbage-In/Garbage-Out Paradox, the second of which (Bayesian synthesis) violates the Borel Paradox, and the third of which (Bayesian melding) is a supra-Bayesian heuristic. This paper shows how to derive a fully Bayesian formula which avoids the Garbage-In/Garbage-Out and Borel Paradoxes. We also compare a Laplacian approximation of this formula with Bayesian synthesis and Bayesian melding and find that the Bayesian formula sometimes coincides with the Bayesian melding solution. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Robert Bordley, 2015. "Avoiding both the Garbage-In/Garbage-Out and the Borel Paradox in updating probabilities given experimental information," Theory and Decision, Springer, vol. 79(1), pages 95-105, July.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:1:p:95-105
    DOI: 10.1007/s11238-013-9369-0
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    References listed on IDEAS

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    1. Schweder, T. & Hjort, N.L., 1996. "Bayesian Synthesis or Likelihood Synthesis - What Does the Borel Paradox Say?," Memorandum 1996_013, Oslo University, Department of Economics.
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