Markov chain geostatistics

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Markov chain geostatistics refer to the Markov chain models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional field for 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 a location through interactions with its nearest known neighbors in different directions, including its last stay location. Because single-step transition probability matrices are difficult to estimate from sparse sample data and are impractical in representing the complex spatial heterogeneity of states, the transiogram, which is defined as a transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.

References[edit]

  1. Li, W. 2007. Markov chain random fields for estimation of categorical variables. Math. Geol., 39(3): 321-335.
  2. Li, W. and C. Zhang. 2007. A random-path Markov chain algorithm for simulating categorical soil variables from random point samples. Soil Sci. Soc. Am. J., 71(3): 656-668.