Professor Alexandre Chorin's Lectures

Prediction and Optimal Prediction PUBLIC LECTURE
Wednesday, November 4, 2009 - 4:00 p.m., Alumni Center Ballroom (refreshments will be served at 3:30 p.m.)

Abstract: There are many problems in science (for example, in climate modelling or in economics) where one has to make long-range forecasts on the basis of uncertain models and data that are noisy and incomplete. I will present a mathematical analysis of how this can be done optimally. One moral of this presentation will be that in practice many predictions are invalidated, not only by the incompleteness of the models and the data, but also by the use of plausible but erroneous mathematical assumptions to simplify computations.

Non-Bayesian Particle Filters ENGINEERING LECTURE
Tuesday, November 3, 2009 - 3:35 p.m., Engineering, Meteorology and Oceanography Lecture, 101 Love Building (refreshments will be served at 3:00 p.m. in 353 Love Building)

Abstract: Filtering and data assimilation are indispensable tools in engineering, weather forecasting, and other areas where one has to make predictions on the basis of uncertain models supplemented by a stream of uncertain data. In nonlinear problems such filtering can be excessively laborious. I will present a scheme, related to chainless sampling that tames the amount of labor. Its main features are a representation of each new probability density by a set of functions of Gaussian variables (a distinct function for each sample and each step), and a resampling based on normalization constants. Examples will be given.

Monte Carlo without Chains MATHEMATICS LECTURE
Friday, November 6, 2009 - 3:35 p.m., Mathematics Lecture, 101 Love Building (refreshments will be served at 3:00 p.m. in 204 Love Building)

Abstract: Monte Carlo methods are stochastic computing methods which are indispensable in the solution of problems with very many variables. They are almost always based on Markov chains, for good reasons that I will briefly recapitulate. There are many problems, however, where Markov chain Monte Carlo is too slow, and I will present a faster alternative based on renormalization group ideas, with examples from physics.