A Bayesian mixed shrinkage prior procedure for spatial-stochastic basis selection and evaluation of gPC expansions: applications to elliptic SPDEs

DOI10.1016/j.jcp.2014.12.034zbMath1352.65634OpenAlexW2093879565MaRDI QIDQ729029

Guang Lin, Georgios Karagiannis, Bledar A. Konomi

Publication date: 20 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.12.034

zbMATH Keywords

sparse approximationMCMCuncertainty quantificationgeneralized polynomial chaosstochastic PDEBayesian model uncertainty

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Bayesian inference (62F15) Monte Carlo methods (65C05) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (10)

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs ⋮ On the Bayesian calibration of computer model mixtures through experimental data, and the design of predictive models ⋮ Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification ⋮ An adaptive WENO collocation method for differential equations with random coefficients ⋮ Using automatic differentiation for compressive sensing in uncertainty quantification ⋮ Bayesian wavelet shrinkage with beta priors ⋮ Enhancing sparsity of Hermite polynomial expansions by iterative rotations ⋮ Spectral likelihood expansions for Bayesian inference ⋮ Bayesian wavelet shrinkage with logistic prior ⋮ Asymmetric Prior in Wavelet Shrinkage

Uses Software

• blasso
• FRK

Cites Work

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• Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification
• Reweighted \(\ell_1\) minimization method for stochastic elliptic differential equations
• An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
• Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs
• Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
• A non-adapted sparse approximation of PDEs with stochastic inputs
• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Adaptive sparse polynomial chaos expansion based on least angle regression
• Cases for the nugget in modeling computer experiments
• An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
• Sparse high order FEM for elliptic sPDEs
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Simulation methodology - an introduction for queueing theorists
• A practical guide to splines
• Interpolation of spatial data. Some theory for kriging
• Weak convergence and optimal scaling of random walk Metropolis algorithms
• Bayesian model averaging: A tutorial. (with comments and a rejoinder).
• Optimal predictive model selection.
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• Introduction to the constructive theory of functions
• Bayesian Regression with Multivariate Linear Splines
• Sparse Tensor Discretization of Elliptic sPDEs
• Elastic Net Regression Modeling With the Orthant Normal Prior
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Fixed Rank Kriging for Very Large Spatial Data Sets
• The Bayesian Lasso
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window
• Bayesian Compressive Sensing
• Multitask Compressive Sensing
• LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Adaptive Rejection Sampling for Gibbs Sampling
• Equation of State Calculations by Fast Computing Machines
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Solution of stochastic partial differential equations using Galerkin finite element techniques

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