Graphical Models in Data Assimilation

Alexander Ihler
Department of Computer Sciences, University of California, Irvine

In data assimilation of a time series, one incorporates past and current observations with a model of system dynamics, so as to improve the model's subsequent simulation or predictions. From a statistical point of view, this can be regarded as a process of estimating a collection of random variables (representing the state of the physical system) which are related both spatially and temporally. Given values for some of these variables (typically times past) we require estimates of others (typically corresponding to future times, or to variables which cannot be directly observed).

Graphical models have emerged as an effective formalism for assisting in these types of inference tasks, particularly for large numbers of random variables. Graphical models provide a means of representing the structure of dependencies among the variables. This structure can be used to construct efficient algorithms for optimal or approximate estimation and other inference tasks. We describe several examples of how graphical models have been applied to data assimilation problems, including Markov chains and Kalman filtering for optimal estimation in time series, multi-resolution models for tomography and image processing, and Markov random fields for modelling rainfall patterns in space and time.

Last Update: September 30, 2005