Multivariate Probabilistic Collocation Method for effective uncertainty evaluation with application to air traffic management

Modern large-scale infrastructure systems are typically complicated in nature and require extensive simulations to evaluate their performance. The Probabilistic Collocation Method (PCM) is developed to effectively simulate system performance under uncertainty. In this paper, we extend the formal analysis of the single-variable PCM to the multivariate case, where the parameters may or may not be independent. Specifically, we provide conditions that permit the multivariate PCM to precisely predict the mean of the original system output. We also explore additional capabilities of the multivariate PCM, in terms of cross-statistics prediction, relation to the minimum mean-square estimator, and computational feasibility for large dimensional data. At the end of the paper, we demonstrate the application of the multivariate PCM in air traffic management.