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Author:   Lorenz Biegler (Carnegie Mellon, USA) ,  George Biros (University of Pennsylvania, USA) ,  Omar Ghattas (Univesity of Texas at Austin, USA) ,  Matthias Heinkenschloss (Rice University, USA)
Publisher:   John Wiley & Sons Inc
Imprint:   John Wiley & Sons Inc
Dimensions:   Width: 15.80cm , Height: 2.30cm , Length: 23.60cm
Weight:   0.748kg
ISBN:  

9780470697436

ISBN 10:   0470697431
Pages:   400
Publication Date:   05 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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 10.4 Summary Bibliography 11 The Ensemble Kalman Filter and Related Filters 11.1 Introduction 11.2 Model Assumptions 11.3 The Traditional Kalman Filter (KF) 11.4 The Ensemble Kalman Filter (EnKF) 11.5 The Randomized Maximum Likelihood Filter (RMLF) 11.6 The Particle Filter (PF) 11.7 Closing Remarks 11.8 Appendix A: Properties of the EnKF Algorithm 11.9 Appendix B: Properties of the RMLF Algorithm Bibliography 12 Using the ensemble Kalman Filter for history matching and uncertainty quantification of complex reservoir models 12.1 Introduction 12.2 Formulation and solution of the inverse problem 12.3 EnKF history matching workflow 12.4 Field Case 12.5 Conclusion Bibliography 13 Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of Impedance Imaging 13.1 Introduction 13.2 Impedance Tomography 13.3 Optimal Experimental Design - Background 13.4 Optimal Experimental Design for Nonlinear Ill-Posed Problems 13.5 Optimization Framework 13.6 Numerical Results 13.7 Discussion and Conclusions Bibliography 14 Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach 14.1 Introduction 14.2 Mathematical developments 14.3 Numerical Examples 14.4 Summary Bibliography 15 Uncertainty analysis for seismic inverse problems: two practical examples 15.1 Introduction 15.2 Traveltime inversion for velocity determination. 15.3 Prestack stratigraphic inversion 15.4 Conclusions Bibliography 16 Solution of inverse problems using discrete ODE adjoints 16.1 Introduction 16.2 Runge-Kutta Methods 16.3 Adaptive Steps 16.4 Linear Multistep Methods 16.5 Numerical Results 16.6 Application to Data Assimilation 16.7 Conclusions Bibliography TBD

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Author Information

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.

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