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This book focuses on computational methods for largescale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimizationbased approaches to solving inverse problems. The aim is to crossfertilize the perspectives of researchers in the areas of data assimilation, statistics, largescale optimization, applied and computational mathematics, high performance computing, and cuttingedge applications.The solution to largescale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon stateoftheart methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reducedorder models and emulators of the forward problem, stochastic spectral approximations, and ensemblebased approximations, as well as exploiting the machinery for largescale deterministic optimization through adjoint and other sensitivity analysis methods.Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current stateoftheart and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification.Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
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