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Uncertainty Quantification: Theory, Implementation, and Applications

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By Ralph C. Smith


2014 / xviii + 382 pages / Hardcover / ISBN 978-1-611973-21-1 / List Price $79.00 / SIAM Member Price $55.30 / Order Code CS12

Keywords: uncertainty quantification, model calibration, surrogate models, parameter selection, sensitivity analysis

Errata to the First Printing

SIREV Book Review

This book stands out in its coverage of a broad but connected range of topics in uncertainty quantification. The author addresses an area that is very active in terms of current research and manages to provide a foundation for methods that are becoming well established. Uncertainty Quantification: Theory, Implementation, and Applications does an excellent job of capturing the state of the art." – Karen Willcox, MIT 

The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines.

The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.

Uncertainty Quantification: Theory, Implementation, and Applications includes

  • a large number of definitions and examples that use a suite of relatively simple models to illustrate concepts;
  • numerous references to current and open research issues;
  • exercises that illustrate basic concepts and guide readers through the numerical implementation of algorithms for prototypical problems;
  • a wide range of applications, including weather and climate models, subsurface hydrology and geology models, nuclear power plant design, and models for biological phenomena; and 
  • recent advances and topics that have appeared in the research literature within the last 15 years, including aspects of Bayesian model calibration, surrogate model development, parameter techniques, and global sensitivity analysis. 

Software and related material can be found here.

The text is intended for advanced undergraduates, graduate students, and researchers in mathematics, statistics, operations research, computer science, biology, science, and engineering. It can be used as a textbook for one- or two-semester courses on uncertainty quantification or as a resource for researchers in a wide array of disciplines. A basic knowledge of probability, linear algebra, ordinary and partial differential equations, and introductory numerical analysis techniques is assumed.

About the Author
Ralph C. Smith is a Professor of Mathematics and Associate Director of the Center for Research in Scientific Computation at North Carolina State University.

ISBN 9781611973211

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