View source for Markov chain geostatistics

'''Markov chain geostatistics''' uses [[Markov chain]] spatial models, [[simulation]] [[algorithm]]s and associated spatial [[correlation]] measures (e.g.,  [[:fr:transiogramme|transiogram]]) based on the Markov chain random field theory, which extends a single [[Markov chain]] into a multi-dimensional random field for [[geostatistics|geostatistical modeling]]. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability [[Matrix (mathematics)|matrices]] are difficult to estimate from sparse [[Sample (statistics)|sample]] data and are impractical in representing the complex spatial [[heterogeneity]] of states, the '''[[:fr:transiogramme|transiogram]]''', which is defined as a [[transition probability]] [[Function (mathematics)|function]] over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.

== References ==

# Li, W. 2007. Markov chain random fields for estimation of categorical variables. Math. Geol., 39(3): 321–335.
# Li, W. et al. 2015. Bayesian Markov chain random field cosimulation for improving land cover classification accuracy. Math. Geosci., 47(2): 123–148. 
# Li, W., and C. Zhang. 2019. Markov chain random fields in the perspective of spatial Bayesian networks and optimal neighborhoods for simulation of categorical fields. Computational Geosciences, 23(5): 1087-1106. 
# http://gisweb.grove.ad.uconn.edu/weidong/Markov_chain_spatial_statistics.htm

[[Category:Geostatistics]]
[[Category:Interpolation]]
[[Category:Markov models]]


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