Bayesian and frequentist inequality tests
Year: 2016
Type: preprint
Abstract: Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (and normal). We compare Bayesian and frequentist hypothesis tests of inequality restrictions in such cases. For finite-dimensional parameters, if the null hypothesis is that the parameter vector lies in a certain half-space, then the Bayesian test has (frequentist) size $\alpha$; if the null hypothesis is any other convex subspace, then the Bayesian test has size strictly above $\alpha$; and if the null is non-convex, then the Bayesian test's size may be above or below $\alpha$. For infinite-dimensional parameters, similar results hold. The example of first-order stochastic dominance testing is detailed.
Source: arXiv (Cornell University)
Authors: David M. Kaplan, Longhao Zhuo
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2468024009