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This paper proposes a statistical verification framework using Gaussianprocesses (GPs) for simulation-based verification of stochastic nonlinearsystems with parametric uncertainties. Given a small number of stochasticsimulations, the proposed framework constructs a GP regression model andpredicts the system's performance over the entire set of possibleuncertainties. Included in the framework is a new metric to estimate theconfidence in those predictions based on the variance of the GP's cumulativedistribution function. This variance-based metric forms the basis of activesampling algorithms that aim to minimize prediction error through carefulselection of simulations. In three case studies, the new active samplingalgorithms demonstrate up to a 35% improvement in prediction error over otherapproaches and are able to correctly identify regions with low predictionconfidence through the variance metric.

Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties