A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems under Uncertainty

DOI10.1137/16M1063289zbMath1373.65003OpenAlexW2758243431WikidataQ126243147 ScholiaQ126243147MaRDI QIDQ5358962

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Publication date: 22 September 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1063289

zbMATH Keywords

algorithmnumerical integrationinverse problemserror analysisMonte Carlo methodserror bounduncertainty quantificationadaptive sampling

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Monte Carlo methods (65C05) Measures and integrals in product spaces (28A35) Inverse problems in optimal control (49N45)

Related Items (3)

Goal-oriented adaptive surrogate construction for stochastic inversion ⋮ Data-driven uncertainty quantification for predictive flow and transport modeling using support vector machines ⋮ Adaptive sampling-based quadrature rules for efficient Bayesian prediction

Uses Software

• ADCIRC
• TESTPACK

Cites Work

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• An efficient surrogate-based method for computing rare failure probability
• Evaluation of failure probability via surrogate models
• Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations
• A family of embedded Runge-Kutta formulae
• Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees
• Bifurcation analysis of periodic SEIR and SIR epidemic models
• A multivariate Kolmogorov-Smirnov test of goodness of fit
• Parameter estimation and uncertainty quantification for an epidemic model
• The Mathematics of Infectious Diseases
• A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis
• A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest
• Active Subspaces
• A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
• MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Integral estimation from point cloud in d-dimensional space
• Introduction to Quasi-Monte Carlo Integration and Applications

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