A FixedPath Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables
 Weidong Li
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Get AccessThe Markov chain random field (MCRF) theory provided the theoretical foundation for a nonlinear Markov chain geostatistics. In a MCRF, the single Markov chain is also called a “spatial Markov chain” (SMC). This paper introduces an efficient fixedpath SMC algorithm for conditional simulation of discrete spatial variables (i.e., multinomial classes) on point samples with incorporation of interclass dependencies. The algorithm considers four nearest known neighbors in orthogonal directions. Transiograms are estimated from samples and are modelfitted to provide parameter input to the simulation algorithm. Results from a simulation example show that this efficient method can effectively capture the spatial patterns of the target variable and fairly generate all classes. Because of the incorporation of interclass dependencies in the simulation algorithm, simulated realizations are relatively imitative of each other in patterns. Largescale patterns are well produced in realizations. Spatial uncertainty is visualized as occurrence probability maps, and transition zones between classes are demonstrated by maximum occurrence probability maps. Transiogram analysis shows that the algorithm can reproduce the spatial structure of multinomial classes described by transiograms with some ergodic fluctuations. A special characteristic of the method is that when simulation is conditioned on a number of sample points, simulated transiograms have the tendency to follow the experimental ones, which implies that conditioning sample data play a crucial role in determining spatial patterns of multinomial classes. The efficient algorithm may provide a powerful tool for largescale structure simulation and spatial uncertainty analysis of discrete spatial variables.
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 Title
 A FixedPath Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables
 Journal

Mathematical Geology
Volume 39, Issue 2 , pp 159176
 Cover Date
 20070201
 DOI
 10.1007/s1100400690717
 Print ISSN
 08828121
 Online ISSN
 15738868
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Markov chain random field
 spatial Markov chain
 transiogram
 multinomial classes
 interclass relationship
 nearest known neighbor
 Industry Sectors
 Authors

 Weidong Li ^{(1)}
 Author Affiliations

 1. Department of Geography, Kent State University, 179 Dale Drive, Apt. 204, Kent, OH, 44240, USA