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Double conditioning: the hidden connection between Bayesian and classical statistics

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  • Manganelli, Simone

Abstract

Bayesian decisions are observationally identical to decisions with judgment. Decisions with judgment test whether a judgmental decision is optimal and, in case of rejection, move to the closest boundary of the confidence interval, for a given confidence level. The resulting decisions condition on sample realizations, which are used to construct the confidence interval itself. Bayesian decisions condition on sample realizations twice, with the tested hypothesis and with the choice of the confidence level. The second conditioning reveals that Bayesian decision makers have an ex ante confidence level equal to one, which is equivalent to assuming an uncertainty neutral behavior. Robust Bayesian decisions are characterized by an ex ante confidence level strictly lower than one and are therefore uncertainty averse. JEL Classification: C1, C11, C12, C13

Suggested Citation

  • Manganelli, Simone, 2023. "Double conditioning: the hidden connection between Bayesian and classical statistics," Working Paper Series 2786, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20232786
    Note: 196912
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    References listed on IDEAS

    as
    1. Bewley, Truman F., 2011. "Knightian decision theory and econometric inferences," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1134-1147, May.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    4. Manganelli, Simone, 2021. "Statistical decision functions with judgment," Working Paper Series 2512, European Central Bank.
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    More about this item

    Keywords

    ambiguity aversion; confidence intervals; hypothesis testing; statistical decision theory;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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