MCMC, SMC,... What next ?

The Monte Carlo method was initially developed for scientific computing in statistical physics during the early days of the computers. Due to the rapid progress in computer technology and the need for handling large datasets and complex systems, the past two decades have witnessed a strong surge of interest in Monte Carlo methods from the scientific community. Researchers ranging from computational biologist to signal \& image processing engineers and to financial econometricians now view Monte Carlo techniques as essential tools for inference. Besides using the popular Markov chain Monte Carlo strategies and adaptive variants of it, various sequential Monte Carlo strategies have recently appeared on the scene, resulting in a wealth of novel and effective inferential and optimization tools. In this talk, we will present what we believe to be the "state-of-the art" in Monte-Carlo simulations for inference and will try to identify the next challenges.