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Models of spatial transition probabilities, or equivalently, transiogrammodels have been recently proposed as spatial continuity measures incategorical fields. In this paper, properties of transiogram models areexamined analytically, and three important findings are reported. Firstly,connections between the behaviors of auto-transiogram models near the originand the spatial distribution of the corresponding category are carefullyinvestigated. Secondly, it is demonstrated that for the indicators of excursionsets of Gaussian random fields, most of the commonly used basic mathematicalforms of covariogram models are not eligible for transiograms in most cases; anexception is the exponential distance-decay function and models that areconstructed from it. Finally, a kernel regression method is proposed forefficient, non-parametric joint modeling of auto- and cross-transiograms, whichis particularly useful for situations where the number of categories is large.

On Spatial Transition Probabilities as Continuity Measures in Categorical Fields