  The Savage-Dickey density ratio is a specific expression of the Bayes factor
when testing a precise (equality constrained) hypothesis against an
unrestricted alternative. The expression greatly simplifies the computation of
the Bayes factor at the cost of assuming a specific form of the prior under the
precise hypothesis as a function of the unrestricted prior. A generalization
was proposed by Verdinelli and Wasserman (1995) such that the priors can be
freely specified under both hypotheses while keeping the computational
advantage. This paper presents an extension of this generalization when the
hypothesis has equality as well as order constraints on the parameters of
interest. The methodology is used for a constrained multivariate t test using
the JZS Bayes factor and a constrained hypothesis test under the multinomial
model.
