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Bayesian Inference Does Not Lead You Astray . . . On Average

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  • Kreps, David M.

    (Stanford University)

  • Francetich, Alejandro

Abstract

A decision maker faces an unobserved state of nature. She updates her prior on the state based on the realizations of a signal. In this note, we show that the expected posterior on any given state, taking expectation under the conditional distribution of the signal on this same state, is never lower than the prior on said state. In other words, the expected posterior probability on the true state is never lower than the prior on this state, regardless of what the true state is.
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Suggested Citation

  • Kreps, David M. & Francetich, Alejandro, 2014. "Bayesian Inference Does Not Lead You Astray . . . On Average," Research Papers 3059, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3059
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    File URL: http://www.gsb.stanford.edu/faculty-research/working-papers/bayesian-inference-does-not-lead-you-astrayon-average
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    Cited by:

    1. Alejandro Francetich & David M. Kreps, 2014. "Choosing a Good Toolkit: An Essay in Behavioral Economics," Working Papers 524, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Hart, Sergiu & Rinott, Yosef, 2020. "Posterior probabilities: Dominance and optimism," Economics Letters, Elsevier, vol. 194(C).
    3. Francetich, Alejandro & Kreps, David, 2020. "Choosing a good toolkit, II: Bayes-rule based heuristics," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    4. Navin Kartik & Frances Xu Lee & Wing Suen, 2021. "Information Validates the Prior: A Theorem on Bayesian Updating and Applications," American Economic Review: Insights, American Economic Association, vol. 3(2), pages 165-182, June.
    5. Sergiu Hart & Yosef Rinott, 2022. "Posterior Probabilities: Nonmonotonicity, Asymptotic Rates, Log-Concavity, and Tur\'an's Inequality," Papers 2209.11728, arXiv.org.

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