Handbook of Uncertainty Quantification

1. Front Matter

   Pages i-xxv

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2. Introduction to Uncertainty Quantification

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction to Uncertainty Quantification

      • Roger Ghanem, David Higdon, Houman Owhadi

      Pages 3-6

3. Methodology

   1. Front Matter

      Pages 7-7

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   2. Bayes Linear Emulation, History Matching, and Forecasting for Complex Computer Simulators

      • Michael Goldstein, Nathan Huntley

      Pages 9-32

   3. Inference Given Summary Statistics

      • Habib N. Najm, Kenny Chowdhary

      Pages 33-67

   4. Multi-response Approach to Improving Identifiability in Model Calibration

      • Zhen Jiang, Paul D. Arendt, Daniel W. Apley, Wei Chen

      Pages 69-127

   5. Validation of Physical Models in the Presence of Uncertainty

      • Robert D. Moser, Todd A. Oliver

      Pages 129-156

   6. Toward Machine Wald

      • Houman Owhadi, Clint Scovel

      Pages 157-191

   7. Hierarchical Models for Uncertainty Quantification: An Overview

      • Christopher K. Wikle

      Pages 193-218

   8. Random Matrix Models and Nonparametric Method for Uncertainty Quantification

      • Christian Soize

      Pages 219-287

   9. Maximin Sliced Latin Hypercube Designs with Application to Cross Validating Prediction Error

      • Yan Chen, David M. Steinberg, Peter Qian

      Pages 289-309

   10. The Bayesian Approach to Inverse Problems

       • Masoumeh Dashti, Andrew M. Stuart

       Pages 311-428

   11. Multilevel Uncertainty Integration

       • Sankaran Mahadevan, Shankar Sankararaman, Chenzhao Li

       Pages 429-475

   12. Bayesian Cubic Spline in Computer Experiments

       • Yijie Dylan Wang, C. F. Jeff Wu

       Pages 477-495

   13. Propagation of Stochasticity in Heterogeneous Media and Applications to Uncertainty Quantification

       • Guillaume Bal

       Pages 497-519

   14. Polynomial Chaos: Modeling, Estimation, and Approximation

       • Roger Ghanem, John Red-Horse

       Pages 521-551

4. Forward Problems

   1. Front Matter

      Pages 553-553

      PDF

   2. Bayesian Uncertainty Propagation Using Gaussian Processes

      • Ilias Bilionis, Nicholas Zabaras

      Pages 555-599

   3. Solution Algorithms for Stochastic Galerkin Discretizations of Differential Equations with Random Data

      • Howard Elman

      Pages 601-616

The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.      

• Polynomial Chaos
• Risk Analysis
• Risk Models
• Sensitivity Analysis
• Uncertainty Quantification

       

• Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA

  Roger Ghanem

• Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, USA

  David Higdon

• Computing and Mathematical Sciences, California Institute of Technology, Pasadena, USA

  Houman Owhadi

Roger Ghanem is the Gordon S. Marshall Professor of Engineering at the University of Southern California where he holds joint appointments in the Departments of Civil & Environmental Engineering and Mechanical & Aerospace Engineering.

David Higdon is Scientists and Group Leader in Statistical Sciences at Los Alamos National Laboratories. He has developed statistical concepts and methodologies that are uniquely adapted to modeling and simulation and computationally intensive numerical models

Houman Owhadi is a Professor of Applied & Computational Mathematics and Control & Dynamical Systems at the California Institute of Technology.    

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