Uncertainty Quantification: Theory, Implementation, and Applications (Computational Science and Engineering) - Hardcover

Smith, Ralph

Hardcover

ISBN 10: 161197321X ISBN 13: 9781611973211

Publisher: Society for Industrial and Applied Mathematics, 2014

Synopsis

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; and exercises that illustrate basic concepts and guide readers through the numerical implementation of algorithms for prototypical problems. It also features a wide range of applications, including weather and climate models, subsurface hydrology and geology models, nuclear power plant design, and models for biological phenomena, along with 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 selection techniques, and global sensitivity analysis.

Audience: 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.

Contents: Chapter 1: Introduction; Chapter 2: Large-Scale Applications; Chapter 3: Prototypical Models; Chapter 4: Fundamentals of Probability, Random Processes, and Statistics; Chapter 5: Representation of Random Inputs; Chapter 6: Parameter Selection Techniques; Chapter 7: Frequentist Techniques for Parameter Estimation; Chapter 8: Bayesian Techniques for Parameter Estimation; Chapter 9: Uncertainty Propagation in Models; Chapter 10: Stochastic Spectral Methods; Chapter 11: Sparse Grid Quadrature and Interpolation Techniques; Chapter 12: Prediction in the Presence of Model Discrepancy; Chapter 13: Surrogate Models; Chapter 14: Local Sensitivity Analysis; Chapter 15: Global Sensitivity Analysis; Appendix A: Concepts from Functional Analysis; Bibliography; Index

About this title

Book Description

Intended for students at the advanced undergraduate level plus and researchers, this book develops the probability theory, statistics and algorithm design necessary to quantify input and response uncertainties for simulation models. The book explores applications and open research problems from fields such as climate science, hydrology, and nuclear power.

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.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2014
• ISBN 10: 161197321X
• ISBN 13: 9781611973211
• Binding: Hardcover
• Language: English
• Number of pages: 400