Graphical Models for Statistical Inference and Data Assimilation

Title:

Graphical Models for Statistical Inference and Data Assimilation

Author(s):

Ihler, Alexander T.
Kirshner, Sergey
Ghil, Michael
Robertson, Andrew W.
Smyth, Padhraic

Date:

2007

Type:

Articles

Department:

International Research Institute for Climate and Society

Volume:

230

Permanent URL:

http://hdl.handle.net/10022/AC:P:14199

Book/Journal Title:

Physica D: Nonlinear Phenomena

Abstract:

In data assimilation for a system which evolves in time, one combines past and current observations with a model of the dynamics of the system, in order to improve the simulation of the system as well as any future predictions about it. From a statistical point of view, this process can be regarded as estimating many random variables, which are related both spatially and temporally: given observations of some of these variables, typically corresponding to times past, we require estimates of several others, typically corresponding to future times. 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 dependency structure among the variables, and can provide both intuition and efficiency in estimation and other inference computations. We provide an overview and introduction to graphical models, and describe how they can be used to represent statistical dependency and how the resulting structure can be used to organize computation. The relation between statistical inference using graphical models and optimal sequential estimation algorithms such as Kalman filtering is discussed. We then give several additional examples of how graphical models can be applied to climate dynamics, specifically estimation using multiresolution models of largescale data sets such as satellite imagery, and learning hidden Markov models to capture rainfall patterns in space and time.

Subject(s):

Meteorology

Publisher DOI:

http://dx.doi.org/10.1016/j.physd.2006.08.023
 Item views:

200
 Metadata:

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 Suggested Citation:

Alexander T. Ihler, Sergey Kirshner, Michael Ghil, Andrew W. Robertson, Padhraic Smyth,
2007,
Graphical Models for Statistical Inference and Data Assimilation, Columbia University Academic Commons,
http://hdl.handle.net/10022/AC:P:14199.