Particle Filters for nonlinear data assimilation in high-dimensional systems

Abstract

Particle Filters are Monte-Carlo methods used for Bayesian Inference. Bayesian Inference is based on Bayes Theorem that states how prior information about a system, encoded in a probability density function, is updated when new information in the form of observations of that system become available. This process is called data assimilation in the geosciences. This contribution discusses what particle filters are and what the main issue is when trying to use them in the geosciences, in which the data-assimilation problem is typically very high dimensional. An example is numerical weather forecasting, with a state-space size of a billion or more. Then it discusses recent progress made in trying to beat the so-called 'curse of dimensionality', such as localisation and clever ways to slightly change the model equations to obtain better approximations to the posterior probability density via so-called proposal densities. This culminates in a new class of particle filters that is indeed able to provide estimates of the posterior probability density. The emphasis is not on mathematical rigour but on conveying the main new ideas in this rapidly growing field.