Model uncertainty and model inaccuracy

The problem of model uncertainty versus model inaccuracy is examined in the light of the concept of the ‘probability of correctness of a model under a given context’ introduced by Apostolakis. To avoid possible difficulties linked with this concept, a distinction is introduced between ‘predictive’ models and ‘constitutive’ models, the former being generic in the sense that they can host the latter as submodels. A metric or distance between linear models as well as an objective of the model are introduced, from which we can give an operational definition of ‘model uncertainty’ (with respect to distribution of parameters of the associated constitutive models) and of ‘model accuracy’ with respect to a reference model. Finally the choice of a predictive model is linked to a loss function and a cost of using or defining a model.