In a variety of disciplines including atmospheric sciences, large numerical simulations have become a fundamental scientific tool. A key problem is then how to inform or update such simulations in real time with large numbers of noisy observations, especially when many of the predicted variables are unobserved or the observed quantities bear a complex relation to the predicted variables. In principle, Bayesian
methods provide a solution to this state-estimation problem, but evolving and updating the required probability distributions are problematic in practice as the most straightforward approaches require computations of overwhelming size. This talk will introduce some of the recent ensemble-based or Monte-Carlo approaches for state and parameter estimation in atmospheric sciences. Applications of these methods to a
variety of phenomena ranging from sea-breeze circulations to severe weather and hurricanes will be presented.