We are interested in computing the expectation of a functional of a PDE solution under a
Bayesian posterior distribution. Using Bayes's rule, we reduce the problem to estimating the …

A standard problem in uncertainty quantification and in computational statistics is the
sampling of stationary Gaussian random fields with given covariance in a d-dimensional …

We propose an approximation method for high-dimensional 1-periodic functions based on
the multivariate ANOVA decomposition. We provide analysis of classical ANOVA …

In this paper we apply the previously introduced approximation method based on the
analysis of variance (ANOVA) decomposition and Grouped Transformations to synthetic and …

We propose and analyze several multilevel algorithms for the fast simulation of possibly
nonstationary Gaussian random fields (GRFs) indexed, for example, by the closure of a …

In this paper we propose a method for the approximation of high-dimensional functions over
finite intervals with respect to complete orthonormal systems of polynomials. An important …

We analyze the convergence rate of a multilevel quasi-Monte Carlo (MLQMC) Finite
Element Method (FEM) for a scalar diffusion equation with log-Gaussian, isotropic …

There has been a surge of interest in uncertainty quantification for parametric partial
differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains …

Partial differential equations (PDEs) with uncertain or random inputs have been considered
in many studies of uncertainty quantification. In forward uncertainty quantification, one is …

We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of
wave propagation modeled by the Helmholtz equation in a bounded region in which the …