Short Course on Inverse Modeling

References

Forward UQ

• Ghanem & Spanos, Stochastic finite elements: a spectral approach, 2003

• Xiu, Numerical methods for stochastic computations: a spectral method approach, 2010

• Koehler & Owen, Computer Experiments, 1996

• Oden, Moser and Ghattas, Computer Predictions with Quantified Uncertainty Part I & Part II

• Kennedy and O'Hagan, Bayesian Calibration of Computer Models, 2001

Inverse UQ: Inverse Modeling

• Aster, Borchersi & Thurber, Parameter Estimation and Inverse Problems (3rd Ed), Elsevier, 2018

• Menke, Geophysical Data Analysis: Discrete Inverse Theory (4th Ed.), Academic Press, 2018

• Hansen, Discrete Inverse Problems: Insight and Algorithms, SIAM, 2010

• Oliver, Reynolds & Liu, Inverse Theory for Petroleum Reservoir Characterization and Histroy Matching, Cambridge University Press, 2008

• Tenorio, An introduction to Data Uncertainty and Uncertainty Quantification for Inverse Problems, SIAM, 2017

• Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 2005 a free copy of the book available

• Kaipio & Somersalo, Statistical and Computational Inverse Problems, Springer, 2005

• Parker, Geophysical Inverse Theory, Princeton Press, 1994

Inverse UQ: Data Assimiliation

• Zarchan and Musoff, Fundamentals of Kalman Filtering - A Practical Approach (4th Ed.), AIAA, 2015

• Evensen, Data Assimilation: The Ensemble Kalman Filter (2nd Ed.), Springer, 2009

• Kalnay, Atmostpheric Modeling, Data Assimiliation, and Predictability, Cambridge University, 2003

• NCAR-DAReS-DART: NCAR's Data Assimilation Research Testbed https:dart.ucar.edu/

Reviews

Linear Algebra

• Petersen and Pedersen, The Matrix Cookbook

• Strang, Linear Algebra and Learning from Data, Wellesley Cambridge Press, 2019

Probability/Statistics

• Jaynes, Probability Theory: The logic of science, Cambridge University Press, 2003 & Aubrey Clayton's Lectures on Jaynes’ book

• Gelman, Carlin, Stern, Dunson, Vehtari and Rubin, Bayesian Data Anaysis, CRC Press, 2014 (pdf available for non-commerical purposes)

• Hastie, Tibshirani and Friedman, The Elements of Statistical Learning, Springer, 2009

• Diaconis and Skyrms, Ten great ideas about chance. Princeton University Press, 2019

• Sivia and Skilling, Data Analysis: a Bayesian Tutorial, Oxford University Press, 2006

• Rasmussen and Williams, Gaussian Processes for Machine Learning, MIT press, 2006

• MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003

Python

Learn Python by teaching Karel the Robot from Stanford CS 160A

ETC

Hearly, Data Visualization: A practical introduction, Princeton University Press, 2018