 
Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Spring 2008 Seminar Series
Presents
Uncertainty Analysis in Dynamical Systems
Igor Mezic
University of California, Santa Barbara
Friday, April 11, 2008 3:004:00pm Harold Frank Hall 1104
Abstract:
Uncertainty is measured in many different ways in different fields. The most
popular ways of assessing uncertainty are through variance of a probability
distribution or its informationtheoretic entropy. There is however, a very
natural notion of uncertainty of a probability distribution: uncertainty can
be thought of as a "distance to a certain distribution". I will take this notion
and formalize it to show how it leads to measures of uncertainty that have
some interesting properties. The formalism plays with metric and measure
theoretic properties of the underlying problem. In fact, Shannon entropy is
shown to stem from this analysis, but it is revealed that its metric structure is
trivial. I will then describe how uncertainty evolves in time under the action
of a dynamical system, where no assumptions of linearity or Gaussianity
