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 the 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.

Model Validation is at the heart of the System Identification process. Recently, much renewed interest has been expressed in so called "identification for control". This means that the design variables associated with the identification process are tailored to achieve models that are well suited for control design purposes. A separate, but closely related issue is to devise validation tests that give information about the model's quality and suitability for control design. This paper shows and discusses how a basic and classical residual test gives such information. ------------------------------------------------------------------------------- + Department of Electrical Engineering, Linkoping University, Linkoping, S-58183, Sweden. Email: Ljung@isy.liu.se, Fax: (+46)13 282622. ++ Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, P.R.China. Email: Lguo@iss03.iss.ac.cn, Fax: (86-10)2587343. 1 Introduction "Identification for Control" has since long been of m...