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

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  • Alejandro Francetich
  • David Kreps

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.

Suggested Citation

  • Alejandro Francetich & David Kreps, 2014. "Bayesian Inference Does Not Lead You Astray... On Average," Working Papers 514, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:514
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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. Sergiu Hart & Yosef Rinott, 2022. "Posterior Probabilities: Nonmonotonicity, Asymptotic Rates, Log-Concavity, and Tur\'an's Inequality," Papers 2209.11728, arXiv.org.
    3. Hart, Sergiu & Rinott, Yosef, 2020. "Posterior probabilities: Dominance and optimism," Economics Letters, Elsevier, vol. 194(C).
    4. Francetich, Alejandro & Kreps, David, 2020. "Choosing a good toolkit, II: Bayes-rule based heuristics," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    5. 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.

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