A comparative study of nonlinear Markov chain models for conditional simulation of multinomial classes from regular samples |
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| Authors: | Chuanrong Zhang Weidong Li |
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| Institution: | (1) Department of Geography, Kent State University, Kent, OH 44242, USA |
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| Abstract: | Simulating fields of categorical geospatial variables from samples is crucial for many purposes, such as spatial uncertainty
assessment of natural resources distributions. However, effectively simulating complex categorical variables (i.e., multinomial
classes) is difficult because of their nonlinearity and complex interclass relationships. The existing pure Markov chain approach
for simulating multinomial classes has an apparent deficiency—underestimation of small classes, which largely impacts the
usefulness of the approach. The Markov chain random field (MCRF) theory recently proposed supports theoretically sound multi-dimensional
Markov chain models. This paper conducts a comparative study between a MCRF model and the previous Markov chain model for
simulating multinomial classes to demonstrate that the MCRF model effectively solves the small-class underestimation problem.
Simulated results show that the MCRF model fairly produces all classes, generates simulated patterns imitative of the original,
and effectively reproduces input transiograms in realizations. Occurrence probability maps are estimated to visualize the
spatial uncertainty associated with each class and the optimal prediction map. It is concluded that the MCRF model provides
a practically efficient estimator for simulating multinomial classes from grid samples. |
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| Keywords: | Markov chain random field Transiogram Interclass relationship Conditional simulation Categorical variable |
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