000			02261 a2200217 4500
005			20180514112352.0
008			180508b xxu||||| |||| 00| 0 eng d
020			_a9781611974911
040			_cIIT Kanpur
041			_aeng
082			_a515.357 _bT258i
100			_aTenorio, Luis
245			_aAn introduction to data analysis and uncertainty quantification for inverse problems _cLuis Tenorio
260			_bSociety for Industrial and Applied Mathematics (SIAM) _c2017 _aPhiladelphia
300			_aix, 269p
440			_aMathematics in industry / edited by Thomas A. Grandine
520			_aInverse 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:many examples that explain techniques which are useful to address general problems arising in uncertainty quantificationBayesian and non-Bayesian statistical methods and discussions of their complementary roles, andanalysis of a real data set to illustrate the methodology covered throughout the book.
650			_aMathematics
650			_aInverse problems
942			_cBK
999			_c558871 _d558871