COMPOSITE MODELING OF TRANSFER-FUNCTIONS

The problem under consideration is how to estimate the frequency funct ion of a system and the associated estimation error when a set of poss ible model structures is given and then one of them is known to contai n the true system. The ''classical'' solution to this problem is to, f irst, use a consistent model structure selection criterion to discard all but one single structure, second, estimate a model in this structu re and, third, conditioned on the assumption that the chosen structure contains the true system, compute an estimate of the estimation error , For a finite data set, however, one cannot guarantee that the correc t structure is chosen, and this ''structural'' uncertainty is lost in the previously mentioned approach. In this contribution a method is de veloped that combines the frequency function estimates and the estimat ion errors from all possible structures into a joint estimate and esti mation error. Hence, this approach bypasses the structure selection pr oblem, This is accomplished by employing a Bayesian setting,Special at tention is given to the choice of priors. With this approach it is pos sible to benefit from a priori information about the frequency functio n even though the model structure is unknown.