Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
An energy-minimizing interpolation for robust multigrid methods
SIAM Journal on Scientific Computing
On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Interacting sequential Monte Carlo samplers for trans-dimensional simulation
Computational Statistics & Data Analysis
SIAM Journal on Numerical Analysis
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Journal of Computational Physics
A least-squares approximation of partial differential equations with high-dimensional random inputs
Journal of Computational Physics
Journal of Computational Physics
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Journal of Computational Physics
Nonparametric belief propagation
Communications of the ACM
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
Journal of Computational Physics
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Journal of Computational Physics
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We develop a probabilistic graphical model based methodology to efficiently perform uncertainty quantification in the presence of both stochastic input and multiple scales. Both the stochastic input and model responses are treated as random variables in this framework. Their relationships are modeled by graphical models which give explicit factorization of a high-dimensional joint probability distribution. The hyperparameters in the probabilistic model are learned using sequential Monte Carlo (SMC) method, which is superior to standard Markov chain Monte Carlo (MCMC) methods for multi-modal distributions. Finally, we make predictions from the probabilistic graphical model using the belief propagation algorithm. Numerical examples are presented to show the accuracy and efficiency of the predictive capability of the developed graphical model.