O’Malley and Zaslavsky recommend a scaled-inverse-Wishart model, as we discuss in Section 13.3 of our forthcoming book.. (We took the idea from an earlier draft of the O’Malley/Zaslavsky paper.) The idea is to break up the covariance matrix into a diagonal matrix of scale parameters and an unscaled covariance matrix which is given the inverse-Wishart distribution. This larger miodel is still conditionally conjugate on the larger space. The model can be thought of as a generalization of the half-t model that I describe here.