Séminaire
Graphical models provide a general and systematic framework for describing and working with probability models involving large numbers of interacting random variables. We will review the basic concepts behind graphical models, including the specification of joint distributions in the form of sparse graphs, with nodes representing random variables and edges representing dependence relations, and illustrate how a variety of well-known models such as hidden Markov models and Markov random fields can be cast in this form. The talk will discuss how the structure of the underlying graph can be leveraged for the purposes of efficient computation of unobserved quantities of interest, such as point estimates or distributions of model parameters given observed data, or computation of unobserved latent state variables (examples being smoothing and filtering in hidden Markov and Kalman filter models). Applications of these ideas to a number of different climate-related data sets will be used to illustrate the concepts presented in the talk. Time permitting the talk will conclude with a brief review of current trends in the field, including Bayesian non-parametric models and scalable inference techniques for very large data sets.