The role of model validation for assessing the size of the unmodeled dynamics

The problem of assessing the quality of a given, or estimated, model is a central issue in system identification. Various new techniques for estimating bias and variance contributions to the model error have been suggested in recent literature. In this contribution, classical model validation procedures are placed at the focus of our attention. We discuss the principles by which we reach confidence in a model through such validation techniques and also how the distance to a "true" description can be estimated this way. In particular, we stress how the typical model validation procedure gives a direct measure of the model error of the model test without referring to its ensemble properties. Several model error bounds are developed for various assumptions about the disturbances entering the system.