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  • Textbook
  • © 2015

Introduction to Uncertainty Quantification

Authors:

  • One of the first textbooks on the mathematics and statistics of uncertainty quantification

  • Complete with examples and exercises throughout

  • Comprehensive with rigorous mathematical details and proofs, but also intuition and motivation

Part of the book series: Texts in Applied Mathematics (TAM, volume 63)

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eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-23395-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.99
Price excludes VAT (USA)
Hardcover Book USD 109.99
Price excludes VAT (USA)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • T. J. Sullivan
    Pages 1-8
  3. Measure and Probability Theory

    • T. J. Sullivan
    Pages 9-34
  4. Banach and Hilbert Spaces

    • T. J. Sullivan
    Pages 35-54
  5. Optimization Theory

    • T. J. Sullivan
    Pages 55-74
  6. Measures of Information and Uncertainty

    • T. J. Sullivan
    Pages 75-90
  7. Bayesian Inverse Problems

    • T. J. Sullivan
    Pages 91-112
  8. Filtering and Data Assimilation

    • T. J. Sullivan
    Pages 113-131
  9. Orthogonal Polynomials and Applications

    • T. J. Sullivan
    Pages 133-164
  10. Numerical Integration

    • T. J. Sullivan
    Pages 165-195
  11. Sensitivity Analysis and Model Reduction

    • T. J. Sullivan
    Pages 197-222
  12. Spectral Expansions

    • T. J. Sullivan
    Pages 223-249
  13. Stochastic Galerkin Methods

    • T. J. Sullivan
    Pages 251-276
  14. Non-Intrusive Methods

    • T. J. Sullivan
    Pages 277-294
  15. Distributional Uncertainty

    • T. J. Sullivan
    Pages 295-318
  16. Back Matter

    Pages 319-342

About this book

Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation, and numerous application areas in science and engineering. This text provides a framework in which the main objectives of the field of uncertainty quantification are defined, and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favourite problems to understand their strengths and weaknesses, also making the text suitable as a self-study. This text is designed as an introduction to uncertainty quantification for senior undergraduate and graduate students with a mathematical or statistical background, and also for researchers from the mathematical sciences or from applications areas who are interested in the field.

T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015.  Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

Keywords

  • Computational probability
  • Distributional robustness
  • Inverse Problems
  • Model order reduction
  • Sensitivity analysis
  • Spectral expansions
  • Uncertainty Quantification

Reviews

“Book is one of very few that discuss a vast array of topics in the developing field of uncertainty quantification (UQ). … The text is mathematically rigorous, and though the intended audience is the senior undergraduate or early graduate mathematics student … . this is a book I might recommend to students as a reference for topics related to UQ ... . Overall, this introduction to UQ leaves something to be desired. It is well written … .” (Talea L. Mayo, SIAM Review, Vol. 59 (1), March, 2017)

“This book presents a collection of mathematical results related to Uncertainly Quantification (UQ). It is intended as a textbook for senior undergraduate or graduate students with a background in mathematics and statistics. … The book might be suitable for a research seminar where students are exposed for the first time to the mathematics behind UQ.” (Elisabeth Ullmann, Mathematical Reviews, February, 2017)

“This book aims to provide an introduction to the mathematics of the quantification of uncertainty. It is intended for students in mathematics and statistics. In the US this would be a graduate level textbook.” (William J. Satzer, MAA Reviews, maa.org, February, 2016)

Authors and Affiliations

  • Mathematics Institute, University of Warwick, Coventry, United Kingdom

    T.J. Sullivan

About the author

T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

Bibliographic Information

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-23395-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.99
Price excludes VAT (USA)
Hardcover Book USD 109.99
Price excludes VAT (USA)