Sampling and noise
Alexandre Chorin, UC Berkeley

I will review some sampling algorithms with applications to Bayesian estimation and particle filters.Particle filters can collapse, and I will present some theoretical results on the circumstances under which they do.
There is a widely shared belief that particle filters suffer from a ``curse of dimensionality" so that they must collapse if the number of variablesto be estimated is large enough; I will show that this is not so. Particle filters, and data assimilation in general, usually require a priori knowledge of the statistics of the noise. I will show that they can also be used to determine these statistics. (joint work with Ole Hald, Matthias Morzfeld, and Xuemin Tu).