On Assessing Model Adequacy

A procedure is proposed which allows one to assess the adequacy of models to represent objects. Only the class of inverse problems has been considered in detail. The procedure is based on the definition of a vectorial distance between models. It allows one to order models from the standpoint of their adequacy and apply to the problem many results of ordered sets. When the set of models admits a minimum, this generally coincides with the most adequate model. Otherwise, the most adequate model has to be found with the methods of decision theory. The method may sometimes be cumbersome. It is shown, however, that this fact may represent a useful feature of the method. Moreover, it is shown that most of the existing work on the adequacy of models, even if in embryo, agrees quite well with the proposed framework.