Luis Tenorio, Colorado School of Mines

IAMCS Workshop in Large-Scale Inverse Problems and Uncertainty Quantification

February 24-25, 2011

Stephen W. Hawking Auditorium

George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy

Texas A&M University

College Station, Texas

Data Analysis Tools for Uncertainty Quantification of Inverse Problems

We present exploratory data analysis methods to assess inversion estimates using examples based on 1^2- and 1^1-regularization. These methods can be used to reveal the presence of systematic errors such as bias and discretization effects, or to validate assumptions made on the statistical model used in the analysis. The methods include: confidence intervals and bounds for the bias, resampling methods for model validation, and construction of training sets of functions with controlled local regularity.