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.Comment: This version is the accepted manuscript
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