Abstract

Weighted direct samplers, also known as importance samplers, are Monte Carlo algorithms for generating independent, weighted samples from a given target probability distribution.  Such algorithms have a variety of applications in, e.g., data assimilation, state estimation for stochastic and chaotic dynamics, and computational statistical mechanics.  One challenge in designing and implementing 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 implcit samplers, which have been shown to possess a number of nice properties.  In this talk, I will report on an analysis of the variance of implicit samplers in the small-noise limit and describe a simple method (suggested by the analysis) to obtain a higher-order implicit sampler. Time permitting, I will also discuss how these methods can be applied to numerical discretizations of SDEs.  This is joint work with Jonathan Goodman, Andrew Leach, and Matthias Morzfeld.