Frequentist size of Bayesian inequality tests

Working Paper Number: 
WP 18-02

Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (e.g., Gaussian).  For the corresponding limit 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 (sometimes strictly); and in other cases, size may be above, below, or equal to alpha. Two examples illustrate our results:  testing stochastic dominance and testing curvature of a translog cost function.

JEL Codes: 
C11, C12

Longhao Zhuo