Tuesday, November 12, 2013
IST Lunch Bunch
A Calculus for the Optiman Quantification of Uncertainties
Houman Owhadi, Professor of Applied and Computational Mathematics and Control and Dynamical Systems, Caltech
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical estimators (or models), these estimators are still designed ``by humans'' because there is currently no known recipe or algorithm for dividing the design of a statistical estimator into a sequence of arithmetic operations.
Indeed, enabling computers to "think'' as "humans'' have the ability to do when faced with uncertainty is challenging in two major ways:
(1) Finding optimal statistical estimators remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables.
(2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this talk will describe the development of a form of calculus allowing for the manipulation of infinite dimensional information structures and its application to the optimal quantification of uncertainties in complex systems, the investigation of a 250 year old debate surrounding Bayesian Inference, the identification of new Selberg integral formulae and the scientific computation of optimal statistical estimators.