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Frequentist properties of Bayesian inequality tests

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  • Kaplan, David M.
  • Zhuo, Longhao

Abstract

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically. 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 parameter lies in a specified half-space, then the Bayesian test’s size equals α; if the null hypothesis is a subset of a half-space, then size is above α; otherwise, size may be equal to, above, or below α. Rejection probabilities at certain points are also characterized. Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships.

Suggested Citation

  • Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    • Handle: RePEc:eee:econom:v:221:y:2021:i:1:p:312-336
    DOI: 10.1016/j.jeconom.2020.05.015
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    More about this item

    Keywords

    Generalized Bayes rule; Limit experiment; Minimax; Nonstandard inference; Posterior;
    All these keywords.

    JEL classification:

    • 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

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