Markov Chain Random Fields for Estimation of?Categorical Variables |
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| Authors: | Weidong Li |
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| Institution: | (1) Department of Geography, Kent State University, Kent, OH 44242, USA |
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| Abstract: | Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating
categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces
a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation
(or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional
probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general
solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’
theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional
simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models
are nonlinear. |
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| Keywords: | Multi-dimensional Markov chain Markov random field Conditional simulation Interclass relationship Nonlinear Conditional independence |
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