Past Event: Oden Institute Seminar

Particle filters for spatially extended systems

Alexandre Thiery, Assistant Professor, Department of Statistics & Applied Probability, National University of Singapore

Abstract

Data assimilation is the process of combining mathematical models with collected observations in order to make forecasts and quantify the associated uncertainty. In this talk, we will focus on the sequential nature of many DA problems; this context naturally leads to the repeated application of Bayes formula. The particle filter algorithm is a Monte-Carlo based approach that allows a straightforward numerical implementation of these recursive updates. Particle filters rely on importance sampling combined with a re-sampling step in order to propagate a set of particles forward in time; contrarily to other methods such as the Ensemble Kalman Filter (EnKF), particle filters do not rely on Gaussian assumptions and are asymptotically exact. Although consistent, in order to give reliable results (i.e. avoid collapse), particle filters typically require a number of particles that scale exponentially quickly with the (effective) dimension of the state-space; traditional particle filters are consequently unusable for many large scale applications. To make progress, the spatial decorrelation that is inherent to many applied scenarios has to be exploited through localization procedures. In this talk, we review some of the techniques that have recently been developed for this purpose and propose some new extensions. Bio: Alex Thiery is an assistant professor in the department of Statistics & Applied Probability at the National University of Singapore (NUS); before joining NUS, he obtained his PhD from Warwick University (UK). Alex is interested in leveraging Monte-Carlo and variational methods for high-dimensional Bayesian inference, with particular focus on inverse problems and Data-Assimilation.