Frequentist properties of Bayesian inequality tests

David Kaplan and Longhao Zhuo

Abstract: Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist size of a certain Bayesian hypothesis test of (possibly nonlinear) inequalities. If the null hypothesis is that the (possibly infinite-dimensional) parameter lies in a certain half-space, then the Bayesian test's size is $\alpha$; if the null hypothesis is a subset of a half-space, then size is above $\alpha$; and in other cases, size may be above, below, or equal to $\alpha$. Rejection probabilities at certain points in the parameter space are also characterized. Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships.

Date: 2016-07, Revised 2024-07
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Published in Journal of Econometrics 221 (2021) 312-336

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Journal Article: Frequentist properties of Bayesian inequality tests (2021)
Working Paper: Frequentist properties of Bayesian inequality tests (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1607.00393

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