Analysis And Computation For Bayesian Inverse Problems
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Analysis And Computation For Bayesian Inverse Problems
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Author : Matthew M. Dunlop
language : en
Publisher:
Release Date : 2017
Analysis And Computation For Bayesian Inverse Problems written by Matthew M. Dunlop and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Bayesian statistical decision theory categories.
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems
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Author : Luis Tenorio
language : en
Publisher: SIAM
Release Date : 2017-07-06
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems written by Luis Tenorio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
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 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.
Statistical And Computational Inverse Problems
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Author : Jari Kaipio
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Statistical And Computational Inverse Problems written by Jari Kaipio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.
Bayesian Approach To Inverse Problems
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Author : Jérôme Idier
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-01
Bayesian Approach To Inverse Problems written by Jérôme Idier and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.
Computational Methods For Inverse Problems
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Computational Uncertainty Quantification For Inverse Problems
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Author : Johnathan M. Bardsley
language : en
Publisher: SIAM
Release Date : 2018-08-01
Computational Uncertainty Quantification For Inverse Problems written by Johnathan M. Bardsley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-01 with Science categories.
This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB? code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.
Bayesian Scientific Computing
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Author : Daniela Calvetti
language : en
Publisher: Springer Nature
Release Date : 2023-03-09
Bayesian Scientific Computing written by Daniela Calvetti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-09 with Computers categories.
The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider’s view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.
Parameter Estimation And Inverse Problems
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Author : Richard C. Aster
language : en
Publisher: Elsevier
Release Date : 2018-10-16
Parameter Estimation And Inverse Problems written by Richard C. Aster and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-16 with Science categories.
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. - Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method - Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems - Covers updated information on adjoint methods that are presented in an accessible manner
Bayesian Inverse Problems
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Author : Juan Chiachio-Ruano
language : en
Publisher: CRC Press
Release Date : 2021-11-10
Bayesian Inverse Problems written by Juan Chiachio-Ruano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Mathematics categories.
This book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them. Through this book, the reader will learn how this class of methods can be useful to rigorously address a range of engineering problems where empirical data and fundamental knowledge come into play. The book is written for a non-expert audience and it is contributed to by many of the most renowned academic experts in this field.
Mathematical And Computational Modelling Across The Scales
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Author : Pedro Diez
language : en
Publisher: Springer Nature
Release Date : 2025-06-25
Mathematical And Computational Modelling Across The Scales written by Pedro Diez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Computers categories.
Many physical and engineering systems deal with micro-, meso-, macro-, and multi-scale phenomena. The accurate description and the reliable simulation of such phenomena entail major challenges from the point of view of both mathematical modelling and computational engineering. This book covers a selection of challenges related to "Mathematical and Computational Modelling Across the Scales”, stemming from the lecture notes of the XX edition of the Jacques-Louis Lions Spanish-French School in Numerical Simulations in Physics & Engineering. The thematic focus is broad, encompassing mathematical models of complex physical problems, theoretical results on their derivation, and development of numerical methods for their efficient simulation. The contributions of the book include: uncertainty quantification for phenomena at different scales such as epidemic dynamics, medical imaging, and geophysical exploration; structural health monitoring integrating small-scale sensor data in large-scale computational models; frontier numerical methods for the simulation of geophysical and heliophysical dynamics accounting for multi-scale, heterogeneous media; multi-physics, multi-scale models for the mechanobiology of atheroma plaques formation; locomotion models for swimming at the micro-scale; mathematical foundations of quantum mechanics phenomena at the micro-scale. The book is addressed to scientists and engineers, from both academia and industry, interested in the mathematical modelling and numerical simulation of a variety of complex systems in physics and engineering characterised by multiple scales.