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Informationen zum Autor Lorenz Biegler, Carnegie Mellon University, USA. George Biros, Georgia Institute of Technology, USA. Omar Ghattas , University of Texas at Austin, USA. Matthias Heinkenschloss , Rice University, USA. David Keyes , KAUST and Columbia University, USA. Bani Mallick , Texas A&M University, USA. Luis Tenorio , Colorado School of Mines, USA. Bart van Bloemen Waanders , Sandia National Laboratories, USA. Karen Wilcox, Massachusetts Institute of Technology, USA. Youssef Marzouk , Massachusetts Institute of Technology, USA. Klappentext This book focuses on computational methods for large-scale 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 optimization-based approaches to solving inverse problems. Inhaltsverzeichnis 1 Introduction 1.1 Introduction 1.2 Statistical Methods 1.3 Approximation Methods 1.4 Kalman Filtering 1.5 Optimization 2 A Primer of Frequentist and Bayesian Inference in Inverse Problems 2.1 Introduction 2.2 Prior Information and Parameters: What do you know, and what do you want to know? 2.3 Estimators: What can you do with what you measure? 2.4 Performance of estimators: How well can you do? 2.5 Frequentist performance of Bayes estimators for a BNM 2.6 Summary Bibliography 3 Subjective Knowledge or Objective Belief? An Oblique Look to Bayesian Methods 3.1 Introduction 3.2 Belief, information and probability 3.3 Bayes' formula and updating probabilities 3.4 Computed examples involving hypermodels 3.5 Dynamic updating of beliefs 3.6 Discussion Bibliography 4 Bayesian and Geostatistical Approaches to Inverse Problems 4.1 Introduction 4.2 The Bayesian and Frequentist Approaches 4.3 Prior Distribution 4.4 A Geostatistical Approach 4.5 Concluding Bibliography 5 Using the Bayesian Framework to Combine Simulations and Physical Observations for Statistical Inference 5.1 Introduction 5.2 Bayesian Model Formulation 5.3 Application: Cosmic Microwave Background 5.4 Discussion Bibliography 6 Bayesian Partition Models for Subsurface Characterization 6.1 Introduction 6.2 Model equations and problem setting 6.3 Approximation of the response surface using the Bayesian Partition Model and two-stage MCMC 6.4 Numerical results 6.5 Conclusions Bibliography 7 Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems 7.1 Introduction 7.2 Reducing the computational cost of solving statistical inverse problems 7.3 General formulation 7.4 Model reduction 7.5 Stochastic spectral methods 7.6 Illustrative example 7.7 Conclusions Bibliography 8 Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation 8.1 Introduction 8.2 Linear Parabolic Equations 8.3 Bayesian Parameter Estimation 8.4 Concluding Remarks Bibliography 9 Calibration and Uncertainty Analysis for Computer Simulations with Multivariate Output 9.1 Introduction 9.2 Gaussian Process Models 9.3 Bayesian Model Calibration 9.4 Case Study: Thermal Simulation of Decomposing Foam 9.5 Conclusions Bibliography 10 Bayesian Calibration of Expensive Multivariate Computer Experiments 10.1 Calibration of computer experiments 10.2 Principal component emulation 10.3 Multivariate calibration ...
