Bayesian model selection for a sharp null and a diffuse alternative with econometric applications

In this paper a potential solution is given to the conflict in Bayesian inference between the desire to employ diffuse priors to represent ignorance and the desire to report proper posterior probabilities for alternative models. Using the concept of Stiefel manifolds, diffuse priors are specified on dimension and direction of subspaces of parameter spaces within the context of a linear regression model and a cointegration model. The approach is illustrated using a CAPM and a term structure of interest rates model.