Maximum Entropy Multivariate Analysis of Uncertain Dynamical Systems Based on the Wiener–Askey Polynomial Chaos

Many measurement models are formalized in terms of a stochastic ordinary differential equation that relates its solution to some given observables. The expression of the measurement uncertainty for the solution that is evaluated at some time instants requires the determination of its (joint) probability density function. Recently, the polynomial chaos theory (PCT) has been widely recognized as a promising technique in order to address the problem. The uncertainty estimation via PCT requires the use of a Monte Carlo integration sampling strategy. In this paper, a novel approach will be presented in order to achieve PCT uncertainty estimation on the basis of an analytical methodology, requiring only optimization calculus