Abstract

Co-author: Ramon van Handel (Princeton University)

A problem that arises in many applications is to compute the conditional distributions of stochastic models given observed data. While exact computations are rarely possible, particle filtering algorithms have proved to be very useful for approximating such conditional distributions. Unfortunately, the approximation error of particle filters grows exponentially with dimension, a phenomenon known as curse of dimensionality. This fact has rendered particle filters of limited use in complex data assimilation problems that arise, for example, in weather forecasting. In this talk I will argue that it is possible to develop local particle filtering algorithms whose approximation error is dimension-free. By exploiting conditional decay of correlations properties of high-dimensional models, we prove for the simplest possible algorithm of this type an error bound that is uniform both in time and in the model dimension. (Joint work with R. van Handel)

Related Links: http://arxiv.org/abs/1301.6585 – Preprint