We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative....

We obtain invariant expressions for prior probabilities and priors onthe parameters of nested regression models that are induced by aprior on the parameters of an encompassing linear regression model.The invariance is with respect to specifications that satisfy anecessary set of assumptions....