Dean S. Oliver is the Mewbourne Chair Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma, where he was the Director for four years. Prior to joining the University of Oklahoma, he worked for seventeen years as a research geophysicist, staff reservoir engineer, and research scientist in reservoir characterization for Chevron and for Saudi Aramco. He also spent six years as a professor in the Petroleum Engineering Department at the University of Tulsa. Professor Oliver has been awarded 'best paper of the year' awards from two journals and received the SPE Reservoir Description and Dynamics Award in 2004. He is currently the Executive Editor of the SPE Journal. His research interests are in inverse theory, reservoir characterization, uncertainty quantification, and optimization. Albert C. Reynolds is Professor of Petroleum Engineering and Mathematics, holder of the McMan chair in Petroleum Engineering, and Director of the TUPREP Research Consortium at the University of Tulsa. He has published over 100 technical articles and one previous book, and is well known for his contributions to pressure transient analysis and optimization-based history matching. Professor Reynolds has won the Society of Petroleum Engineers (SPE) Distinguished Achievement Award for Petroleum Engineering Faculty, the SPE Reservoir Description and Dynamics Award, and the SPE Formation Award. He became an SPE Distinguished Member in 1999. Ning Liu holds a Ph.D. from the University of Oklahoma in petroleum engineering and now works as a Reservoir Simulation Consultant at Chevron Energy Technology Company. Dr Liu is a recipient of the Outstanding Ph.D. Scholarship Award at the University of Oklahoma and the Student Research Award from the International Association for Mathematical Geology (IAMG). Her areas of interest are history matching, uncertainty forecasting, production optimization, and reservoir management.

• Preface; 1. Introduction; 2. Examples of inverse problems; 3. Estimation for linear inverse problems; 4. Probability and estimation; 5. Descriptive geostatistics; 6. Data; 7. The maximum a posteriori estimate; 8. Optimization for nonlinear problems using sensitivities; 9. Sensitivity coefficients; 10. Quantifying uncertainty; 11. Recursive methods; Bibliography; Index.

Dean S. Oliver is the Mewbourne Chair Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma, where he was the Director for four years. Prior to joining the University of Oklahoma, he worked for seventeen years as a research geophysicist, staff reservoir engineer, and research scientist in reservoir characterization for Chevron and for Saudi Aramco. He also spent six years as a professor in the Petroleum Engineering Department at the University of Tulsa. Professor Oliver has been awarded 'best paper of the year' awards from two journals and received the SPE Reservoir Description and Dynamics Award in 2004. He is currently the Executive Editor of the SPE Journal. His research interests are in inverse theory, reservoir characterization, uncertainty quantification, and optimization. Albert C. Reynolds is Professor of Petroleum Engineering and Mathematics, holder of the McMan chair in Petroleum Engineering, and Director of the TUPREP Research Consortium at the University of Tulsa. He has published over 100 technical articles and one previous book, and is well known for his contributions to pressure transient analysis and optimization-based history matching. Professor Reynolds has won the Society of Petroleum Engineers (SPE) Distinguished Achievement Award for Petroleum Engineering Faculty, the SPE Reservoir Description and Dynamics Award, and the SPE Formation Award. He became an SPE Distinguished Member in 1999. Ning Liu holds a Ph.D. from the University of Oklahoma in petroleum engineering and now works as a Reservoir Simulation Consultant at Chevron Energy Technology Company. Dr Liu is a recipient of the Outstanding Ph.D. Scholarship Award at the University of Oklahoma and the Student Research Award from the International Association for Mathematical Geology (IAMG). Her areas of interest are history matching, uncertainty forecasting, production optimization, and reservoir management.

• Preface; 1. Introduction; 2. Examples of inverse problems; 3. Estimation for linear inverse problems; 4. Probability and estimation; 5. Descriptive geostatistics; 6. Data; 7. The maximum a posteriori estimate; 8. Optimization for nonlinear problems using sensitivities; 9. Sensitivity coefficients; 10. Quantifying uncertainty; 11. Recursive methods; Bibliography; Index.

Dean S. Oliver is the Mewbourne Chair Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma, where he was the Director for four years. Prior to joining the University of Oklahoma, he worked for seventeen years as a research geophysicist, staff reservoir engineer, and research scientist in reservoir characterization for Chevron and for Saudi Aramco. He also spent six years as a professor in the Petroleum Engineering Department at the University of Tulsa. Professor Oliver has been awarded 'best paper of the year' awards from two journals and received the SPE Reservoir Description and Dynamics Award in 2004. He is currently the Executive Editor of the SPE Journal. His research interests are in inverse theory, reservoir characterization, uncertainty quantification, and optimization. Albert C. Reynolds is Professor of Petroleum Engineering and Mathematics, holder of the McMan chair in Petroleum Engineering, and Director of the TUPREP Research Consortium at the University of Tulsa. He has published over 100 technical articles and one previous book, and is well known for his contributions to pressure transient analysis and optimization-based history matching. Professor Reynolds has won the Society of Petroleum Engineers (SPE) Distinguished Achievement Award for Petroleum Engineering Faculty, the SPE Reservoir Description and Dynamics Award, and the SPE Formation Award. He became an SPE Distinguished Member in 1999. Ning Liu holds a Ph.D. from the University of Oklahoma in petroleum engineering and now works as a Reservoir Simulation Consultant at Chevron Energy Technology Company. Dr Liu is a recipient of the Outstanding Ph.D. Scholarship Award at the University of Oklahoma and the Student Research Award from the International Association for Mathematical Geology (IAMG). Her areas of interest are history matching, uncertainty forecasting, production optimization, and reservoir management.

• Preface; 1. Introduction; 2. Examples of inverse problems; 3. Estimation for linear inverse problems; 4. Probability and estimation; 5. Descriptive geostatistics; 6. Data; 7. The maximum a posteriori estimate; 8. Optimization for nonlinear problems using sensitivities; 9. Sensitivity coefficients; 10. Quantifying uncertainty; 11. Recursive methods; Bibliography; Index.