Implicit sampling in the small-noise limit

Applied and Computational Mathematics Seminar
Monday, November 6, 2017 - 13:55
1 hour (actually 50 minutes)
Skiles 005
University of Arizona
Weighted direct samplers, sometimes also called importance samplers, are Monte Carlo algorithms for generating independent, weighted samples from a given target probability distribution. They are used in, e.g., data assimilation, state estimation for dynamical systems, and computational statistical mechanics. One challenge in designing weighted samplers is to ensure the variance of the weights, and that of the resulting estimator, are well-behaved. Recently, Chorin, Tu, Morzfeld, and coworkers have introduced a class of novel weighted samplers called implicit samplers, which possess a number of nice empirical properties. In this talk, I will summarize an asymptotic analysis of implicit samplers in the small-noise limit and describe a simple method to obtain a higher-order accuracy. I will also discuss extensions to stochastic differential equatons. This is joint work with Jonathan Goodman, Andrew Leach, and Matthias Morzfeld.