Efficient Techniques for Quantifying Uncertainty

Quantifying uncertainty in systems with noisy or unknown parameters is useful in model prediction and design. Stochastic spectral methods are a class of numerical methods designed as an alternative to Monte Carlo for more efficiently quantifying uncertainty via approximation in the random space. Here we introduce the Multi-Element Probabilistic Collocation Method and an extension using an ANOVA-type decomposition, which provide improvement in efficiency and functionality over existing stochastic spectral and Monte Carlo methods. We provide analysis of h/p-type convergence rates as well as numerical examples from applications in physics and biology.