Optimization proxies have the potential to transform various applications through significant improvements in efficiency.
New theoretical and experimental approaches help explain the self-organization of ice under turbulence.
We can trace the evolution of iterative methods up to the present day by examining several pivotal big ideas.
Koopman operator theory has recently emerged as the primary candidate for extracting human-interpretable models from data.
In 2023, SIAM partnered with the Livermore Lab Foundation to support an undergraduate student internship.
Ernest Davis reviews two books about issues of privacy and inequality with facial recognition technologies.
The Hong Kong Polytechnic University SIAM Student Chapter organized an exciting event with experts in the field of optimization.
-
2017 / x + 269 pages / Softcover / ISBN 978-1-611974-91-1 / List Price $69.00 / Member Price $48.30 / Order Code MN03
Keywords: inverse problems, Tikhonov regularization, data analysis, uncertainty quantification, Bayesian inversion
Contents Preface Index
Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics.
This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications.
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems includes
Audience This book is intended for senior undergraduates and beginning graduate students in mathematics, engineering and physical sciences. The material spans from undergraduate statistics and probability to data analysis for inverse problems and probability distributions on infinite-dimensional spaces. It is also intended for researchers working on inverse problems and uncertainty quantification in geophysics, astrophysics, physics, and engineering. Because the statistical and probability methods covered have applications beyond inverse problems, the book may also be of interest to those people working in data science or in other applications of uncertainty quantification. About the Author Luis Tenorio is a faculty member in the Applied Mathematics and Statistics Department at the Colorado School of Mines. He obtained his PhD in mathematics at the University of California at Berkeley and worked on inverse problems in astrophysics as a member of George Smoot's astrophysics group in the Lawrence Berkeley National Laboratory. His main research interests are the statistical aspects of inverse problems with applications to astrophysics and geophysics.
ISBN 9781611974911
View this book