The nonlinear Markov Chain Geostatistics

With the proposition of a Markov chain random field (MCRF) theory and its accompanying spatial measure – the transiogram, Markov chain has been extended into a nonlinear Markov chain-based geostatistical approach for one to multi-dimensional conditional (or unconditional) simulation, called Markov chain geostatistics (MCG). This new approach has nonlinear estimators, considers conditional independence of nearest known neighbors in cardinal directions, and can easily incorporate interclass relationships, which provide it advantages in dealing with categorical variables by generating more imitative patterns and less spatial uncertainty. This paper simply introduces the framework of MCG and recent technological development, and demonstrates some simulated results from MCG.