Title: A Measure Theoretic Computational Approach For Inverse Sensitivity Problems Speaker: Don Estep, Colorado State University, University Interdisciplinary Research Scholar Professor of Mathematics Professor of Statistics Director, CIMS (Center for Interdisciplinary Mathematics and Statistics) Date/Time: Monday, August 30, 2010 at 9:00 – 10:00am Location: International Programs Building (Research Park) Room 1154 Brief Abstract: We consider the probabilistic inverse sensitivity analysis of a map from a set of parameters and data to a quantity of interest. The inverse problem is to describe the random variation in the input and parameters that lead to an imposed or observed random variation on the output quantity. We are interested particularly interested in implicitly-defined maps, e.g. involving the solution of a differential equation. We formulate the problem as an ill-posed inverse problem for an integral equation using the Law of Total Probability and then describe a computational method for computing solutions. The method has two stages. In the first part, we approximate the unique set-valued solution to the inverse of the integral equation using derivative information. In the second part, we apply basic ideas from measure theory to compute the approximate probability measure on the parameter and data space that solves the integral equation. We discuss convergence of the method, and explain how to use the method to compute the probability of events in the input (parameter) space. The talk is illustrated with a number of examples. Time permitting, we discuss briefly the numerical analysis (accuracy) of the method and the consideration of multiple quantities of interest and data assimilation.CSRI POC: John N. Shadid, 505-845-7876 |