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The problem of constructing Bayesian optimal discriminating designs for a class of regression
models with respect to the T-optimality criterion introduced by Atkinson and Fedorov
(1975a) is considered. It is demonstrated that the discretization of the integral with respect
to the prior distribution leads to locally T-optimal discriminating design problems with a
large number of model comparisons. Current methodology for the numerical construction of
discrimination designs can only deal with a few comparisons, but the discretization of the
Bayesian prior easily yields to discrimination design problems for more than 100 competing
models. A new efficient method is developed to deal with problems of this type. It combines
some features of the classical exchange type algorithm with the gradient methods. Convergence
is proved and it is demonstrated that the new method can find Bayesian optimal
discriminating designs in situations where all currently available procedures fail
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