Abstract
We consider a class of finite state, two-dimensional Markov chains which can produce a rich variety of patterns and whose simulation is very fast. A parameterization is chosen to make the process nearly spatially homogeneous. We use a form of pseudo-likelihood estimation which results in quick determination of estimate. Parameters associated with boundary cells are estimated separately. We derive the asymptotic distribution of the maximum pseudo-likelihood estimates and show that the usual form of the variance matrix has to be modified to take account of local dependence. Standard error calculations based on the modified asymptotic variance are supported by a simulation study. The procedure is applied to an eight-state permeability pattern from a section of hydrocarbon reservoir rock.
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Craig, P.S., Seheult, A.H. Pseudo-likelihood estimation for a class of spatial Markov chains. Stat Comput 6, 303–311 (1996). https://doi.org/10.1007/BF00140875
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DOI: https://doi.org/10.1007/BF00140875