  An efficient algorithm for the determination of Bayesian optimal
discriminating designs for competing regression models is developed, where the
main focus is on models with general distributional assumptions beyond the
"classical" case of normally distributed homoscedastic errors. For this purpose
we consider a Bayesian version of the Kullback- Leibler (KL) optimality
criterion introduced by L\'opez-Fidalgo et al. (2007). Discretizing the prior
distribution leads to local KL-optimal discriminating design problems for a
large number of competing models. All currently available methods either
require a large computation time or fail to calculate the optimal
discriminating design, because they can only deal efficiently with a few model
comparisons. In this paper we develop a new algorithm for the determination of
Bayesian optimal discriminating designs with respect to the Kullback-Leibler
criterion. It is demonstrated that the new algorithm is able to calculate the
optimal discriminating designs with reasonable accuracy and computational time
in situations where all currently available procedures are either slow or fail.
