@MISC{Lee_statisticalvalidation, author = {Lawton Lee}, title = {Statistical Validation of Parametric Models}, year = {} }

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Abstract

In this paper we formulate a certain statistical model validation problem where we wish to determine the probability that a certain hypothesized parametric uncertainty model is valid given an experimental input-output data record. We then show that, in many instances of interest, this problem reduces to the computation of relative weighted volumes of convex sets in R N (N being the number of uncertain parameters). Since exact or even approximate volume computation of convex sets in R N is NP -hard, we consider randomized algorithms for determining these validation probabilities. In particular, we present and analyze a randomized algorithm based on gas kinetics for probable approximate computation of these volumes. Sample MATLAB functions are included for reference. 1 Introduction Recently there has been considerable research in the area of control-oriented system identification (see for example [4, 5, 6, 8, 10, 14, 15, 16, 19, 20, 21, 23] and the references cited therein). Thi...