03960nam 2200529 i 45000010014000000030005000140050017000190060019000360070015000550080041000700100017001110200030001280200025001580280015001830350025001980350021002230400040002440500025002840820017003091000028003262450150003542640150005043000026006543360021006803370026007013380032007274900028007595040051007875050320008385060072011585201594012305300037028245380036028615380047028975880054029446500046029986500026030446530021030706530028030916530018031196530031031376530023031687100064031917760053032558300057033088560065033659781611974928SIAM20170619190106.0m eo d cr bn |||m|||a170616s2017 pau ob 001 0 eng d a 2017016391 a9781611974928qelectronic z9781611974911qprint50aMN03bSIAM a(CaBNVSL)thg00974393 a(OCoLC)990266006 aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA378.5b.T46 2017eb04a515/.3572231 aTenorio, Luis,eauthor.13aAn introduction to data analysis and uncertainty quantification for inverse problems /cLuis Tenorio, Colorado School of Mines, Golden, Colorado. 1aPhiladelphia, Pennsylvania :bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),c[2017] a1 PDF (x, 269 pages). atext2rdacontent aelectronic2isbdmedia aonline resource2rdacarrier1 aMathematics in industry aIncludes bibliographical references and index.0 aPreface -- 1. An introduction to inverse problems -- 2. A primer on statistical methods -- 3. Applications to inverse problems I -- 4. Applications to inverse problems II -- 5. A nonlinear parameter estimation problem -- Appendix A. Some results from analysis -- Appendix B. Conditional probability and expectation. aRestricted to subscribers or individual electronic text purchasers.3 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 quantification,Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book. aAlso available in print version. aMode of access: World Wide Web. aSystem requirements: Adobe Acrobat Reader. aDescription based on title page of print version. 0aInverse problems (Differential equations) 0aParameter estimation. aInverse problems aTikhonov regularization aData analysis aUncertainty quantification aBayesian inversion2 aSociety for Industrial and Applied Mathematics,epublisher.08iPrint version:w(DLC) 2017012790z9781611974911 0aMathematics in industry (Philadelphia, Pennsylvania)403SIAMuhttp://epubs.siam.org/doi/book/10.1137/1.9781611974928