The first part of this talk will provide a tutorial overview of a general class of probabilistic models known as graphical models. Graphical models provide a general language for both (a) representing complex sets of dependency relationships among random variables, and (b) providing a systematic framework for computing quantities of interest with such models such as conditional expectations and forecasts. We will see how state-based models, that sequentially combine observations at time t with model-based predictions from time t-1 (including Kalman filters and hidden Markov models), fit naturally within this framework and computational algorithms for such models arise "automatically". In the second part of the talk we will look at more recent research developments in graphical models for sequential data, including development of models with richer representations and development of faster computational methods. Examples and illustrations from the geosciences will be used for motivation and illustration as appropriate.
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