Double conditioning: the hidden connection between Bayesian and classical statistics

Simone Manganelli

No 2786, Working Paper Series from European Central Bank

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

Keywords: ambiguity aversion; confidence intervals; hypothesis testing; statistical decision theory (search for similar items in EconPapers)
Date: 2023-02
New Economics Papers: this item is included in nep-ecm and nep-upt
Note: 196912
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Persistent link: https://EconPapers.repec.org/RePEc:ecb:ecbwps:20232786

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