Solving stochastic inverse problems using sigma-algebras on contour maps
Date and time:
Friday, September 26, 2014 - 3:00pm
We describe recent work on the formulation and numerical solution of stochastic inverse problems for determining parameters in differentialmequations with stochastic data on output quantities. The new approachminvolves approximating the generalized contour maps representingmset-valued inverse solutions, using the approximate contour maps tomdefine a geometric structure on events in the sigma-algebra for the probability space on the parameter domain, and exploiting the structure to define and approximate probability distributions in the space. We will present various examples, including high-dimensional problems involving spatially varying parameter fields in storm surge models.