| In many branches of science one encounters the need to generate samples from high dimensional probability distributions with strong spatial correlations. The usual tools for sampling from such distributions, Markov chain Monte Carlo methods, often make very local steps through configuration space and can, therefore, be inefficient.;In this thesis I propose a new method, parallel marginalization, that uses approximations to successive marginal densities to accelerate MCMC techniques for complex systems. The effectiveness of parallel marginalization stems from its accurate incorporation of information from rapidly equilibrating lower dimensional chains. Its performance has been tested on nonlinear filtering and smoothing problems for stochastic ordinary and partial differential equations. |
