Graphical Models for Statistical Inference and Data Assimilation
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 multi-resolution models of large-scale data sets such as satellite imagery, and learning hidden Markov models to capture rainfall patterns in space and time.
AC:P:14199
Academic Commons
Physica D: Nonlinear Phenomena
0167-2789
10.1016/j.physd.2006.08.023
230
1-2
2007
72
87
Ihler, Alexander T.
Author
Kirshner, Sergey
Author
Ghil, Michael
Author
Robertson, Andrew W.
Author
Smyth, Padhraic
Author
Columbia University. International Research Institute for Climate and Society
Originator
Articles
English
Graphical modeling (Statistics)
Mathematical statistics
Meteorology
text
Elsevier
2007
manuscript version
eng
2012-07-23T16:08:58Z
2018-02-17T00:18:34Z
10.7916/D85T3W4J