Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
SIAM Journal on Scientific Computing
Extensions of the conjugate prior through the Kullback-Leibler separators
Journal of Multivariate Analysis
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
A critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation (or full joint distribution) of uncertain model parameters. In this paper we describe a framework and a class of algorithms for analyzing such ''missing data'' problems in the setting of Bayesian statistics. The analysis focuses on the family of posterior distributions consistent with given statistics (e.g. nominal values, confidence intervals). The combining of consistent distributions is addressed via techniques from the opinion pooling literature. The developed approach allows subsequent propagation of uncertainty in model inputs consistent with reported statistics, in the absence of data.