ON STATISTICAL-MODEL VALIDATION

In this paper we formulate a particular statistical model validation p roblem in which we wish to determine the probability that a certain hy pothesized parametric uncertainty model is consistent with a given inp ut-output data record. Using a Bayesian approach and ideas from the fi eld of hypothesis testing, we show that in many cases of interest this problem reduces to computing relative weighted volumes of convex sets in R(N) (where N is the number of uncertain parameters). We also pres ent and discuss a randomized algorithm based on gas kinetics, as well as the existing Hit-and-Run family of algorithms, for probable approxi mate computation of these volumes.