Title Computational Uncertainty Quantification for Inverse Problems
Subtitle
Author Johnathan M. Bardsley
ISBN 9781611975376
List price USD 59.00
Price outside India Available on Request
Original price
Binding Paperback
No of pages 136
Book size 153 x 229 mm
Publishing year 2018
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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Description:

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.


Contents:

Preface

Chapter 1: Characteristics of Inverse Problems • Preliminaries • The least squares estimator • The statistical properties of xLS and ill-posedness • An illustrative example • Exercises

Chapter 2: Regularization by Spectral Filtering • Spectral filtering methods • Regularization parameter selection methods • Periodic and data-driven boundary conditions • Exercises

Chapter 3: Two-Dimensional Test Cases • Two-dimensional image deblurring • Computed tomography • The preconditioned conjugate gradient iteration • Exercises

Chapter 4: Bayes’  Law, Markov Random Field Priors, and MAP Estimation • Bayes’  law and regularization • Choosing p(x|d): Gaussian Markov random fields • Choosing p(x|d): Laplace Markov random fields • The infinite-dimensional limit • Exercises

Chapter 5: Markov Chain Monte Carlo Methods for Linear Inverse Problems • Sampling from high-dimensional Gaussian random vectors • Hierarchical modeling of ? and d and sampling from p(x, ?, d|b) • Alternative MCMC methods for sampling from p(x, ?, d|b) • Exercises

Chapter 6: Markov Chain Monte Carlo Methods for Nonlinear Inverse Problems • A general setup for nonlinear inverse problems • Levenburg–Marquardt nonlinear least squares optimization • Randomize-then-optimize as a proposal for Metropolis–Hastings • Nonlinear test cases • Hierarchical modeling of ? and d and sampling from p(x, ?, d|b) • Exercises

Bibliography

Index


About the Author:

Johnathan M. Bardsley is a professor in the Department of Mathematical Sciences at the University of Montana, where he has been teaching since 2003. He has held long-term visiting professorships at the University of Helsinki, Finland; University of Otago, New Zealand; Technical University of Denmark; and Monash University, Australia, supported by the Gordon Preston Sabbatical Fellowship. Professor Bardsley was a postdoctoral fellow at the NSF-funded Statistical and Applied Mathematical Sciences Institute during its inaugural year in 2002–03. In 2017, he received the Chancellor’s Medallion Award from Montana Tech for excellence in his educational and professional career and for significant contributions to his academic discipline. Professor Bardsley’s research interests focus on inverse problems, uncertainty quantification, computational mathematics, and computational statistics, and he has published many refereed journal articles in these areas.


Target Audience:

This book 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.

 

 
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