A New Probabilistic Adjoint Operator (Prado) Method for Scalar Observables: Application to Stochastic Electromagnetic Interactions

We describe a stochastic method to characterize uncertainties in numerical models that have a single real-valued output (observable). The rationale estimates the probability density function (PDF) of the observable by inverting the characteristic function (CF), which is computed by quadrature. This approach is seldom used due to the highly oscillatory integrals that define the CF, which cause traditional quadrature algorithms to fail. Instead, we overcome these high oscillations by using an oscillatory Levin quadrature algorithm. We specifically choose the implementation proposed by Webster and Evans for the one-dimensional case and generalize it to the multivariate case. Using the Webster-Evans/Levin rule (WEL), we build a probabilistic adjoint operator (PrAdO).