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Uncertainty Quantification and Stochastic Modeling with Matlab

Eduardo Souza de Cursi and Rubens Sampaio
Publisher: 
Elsevier
Publication Date: 
2015
Number of Pages: 
442
Format: 
Hardcover
Price: 
185.00
ISBN: 
9781785480058
Category: 
Textbook
[Reviewed by
Chris Thron
, on
03/2/2016
]

“I’ve been doing Uncertainty Quantification for years, just without capitals.” This quote from Bill Browning sums up both the established pedigree and recent popularity of Uncertainty Quantification within applied mathematics. The recent resurgence of interest is due to the explosive growth in variety, size, and complexity of simulations, which require new methods to characterize their behavior. Such methods are inevitably stochastic and computationally intensive.

Uncertainty Quantification and Stochastic Modeling with Matlab, by de Cursi and Sampaio, provides both an excellent introduction for newcomers and a practical reference for established practitioners. It begins with a concise but solid introduction to the necessary probability theory (including measure theory, Hilbert space techniques, and stochastic processes) at the graduate student level. It then goes on to treat the construction of probabilistic models, representation of random variables, and application of uncertainty quantification in various regimes of interest: linear and nonlinear equations, differential equations, and optimization. Clear, step-by-step mathematical derivations of basic theoretical results are provided. Practical techniques are illustrated by well-chosen and thoroughly worked-out examples. The included Matlab programs are well-commented and generic enough to be easily translated to other platforms such as Octave, Scilab, Mathematica, or Sage. Numerous Matlab-generated figures (with color versions available online) enhance the quality of the presentation. Overall the style is extremely readable, and the occasional Europeanisms do not significantly distract from the comprehensibility.

The book is not comprehensive (UQ is a vast field); its focus is on straightforward analytical models with parameters that obey known (or estimated) probability distributions. It does not discuss non-analytical models (such as interacting particle, agent-based, or complex models). There is no discussion of Monte Carlo methods, uncertainty propagation, and techniques such as kriging and response surface methodology. The examples are theoretical rather than drawn from real-life applications.

Within its scope, the book has much to offer to a wide variety of readers. Less mathematical, more engineering-oriented, users will appreciate the examples and codes (although such readers would want to steer clear of the dense thickets of mathematical notation); while those of more theoretical bent will appreciate the clear presentation of mathematical foundations, Both types of users will find valuable tools for their respective toolboxes.


Chris Thron has worked as systems engineer for NEC, Motorola, and Freescale, and has been a consultant for Applied Mathematics and MetalNetworks. He is currently associate professor at Texas A&M University-Central Texas, and his current major focus is promoting research and education in computational mathematics and statistics in west central Africa.

1. ELEMENTS OF PROBABILITY THEORY AND STOCHASTIC PROCESSES
2. MAXIMUM ENTROPY AND INFORMATION
3. REPRESENTATION OF RANDOM VARIABLES
4. LINEAR ALGEBRAIC EQUATIONS UNDER UNCERTAINTY
5. NONLINEAR ALGEBRAIC EQUATIONS INVOLVING RANDOM PARAMETERS
6. DIFFERENTIAL EQUATIONS UNDER UNCERTAINTY
7. OPTIMIZATION UNDER UNCERTAINTY
8. RELIABILITY-BASED OPTIMIZATION