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Markov Random Field Models

Spatial and Temporal Modeling and Analysis

  1. Mark S. Kaiser

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vam005

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Kaiser, M. S. 2006. Markov Random Field Models. Encyclopedia of Environmetrics. 3.

Author Information

  1. Iowa State University, IA, USA

Publication History

  1. Published Online: 15 SEP 2006


Statistical models formulated on the basis of Markov random fields (MRFs) constitute an appealing approach to the analysis of data that exhibit complex dependence structures. Such data arise commonly in problems of a spatial or spatiotemporal nature, although MRFs are a general mathematical construct that may be used in other situations such as, for example, the representation of genetic dependence among organisms. Within the context of statistical modeling, a MRF may be defined for any set of random variables defined at a discrete point.