PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Manfred Denker.

Abstract:
Title:	Robust sensitivity analysis for stochastic systems
Seminar:	Seminar on Probability and its Application
Speaker:	Henry Lam, Boston University
Sensitivity analysis for stochastic systems is typically carried out via derivative estimation, which critically requires parametric model assumptions. In many situations, however, we want to evaluate model misspecification effect beyond certain parametric family of models, or in some cases, there plainly are no parametric model to begin with. Motivated by such deficiency, we propose a sensitivity analysis framework that is parameter-free, by using the Kulback-Leibler divergence as a measure of model discrepancy, and obtain well-defined derivative estimators. These estimators are robust in that they automatically choose the worst (and best)-case directions to move along in the (typically infinite-dimensional) model space. They require little knowledge to implement; the distributions of the underlying random variables can be known up to, for example, black-box simulation. Methodologically, we identify these worst-case directions of the model as changes of measure that are the fixed points of a class of functional contraction maps. These fixed points can be asymptotically expanded to obtain derivative estimators that are expressed in closed-form formula in terms of the moments of certain ``symmetrizations" of the system, and hence are readily computable.