A statistical approach to model validation

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