The sequential Monte Carlo (SMC) methodology has shown a great promise in solving a large class of highly complex inference and optimization problems. Although it was originally designed to solve on-line filtering and smoothing of non-linear non-Gaussian state space models, it has been shown to be equally powerful in dealing with fixed-dimensional problems, utilizing a sequential decomposition principle. In this talk we discuss issues and efficient implementations of SMC for dealing with high dimensional distributions that are defined on restricted and ill-shaped spaces. Examples in bioinformatics (RNA and Protein geometric structures) and financial engineering (generating diffusion bridges) are presented.
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