Guofeng Cao ⁺ and Phaedon C. Kyriakidis
_{Department of Geography, University of California Santa Barbara, U.S.A.}

Abstract. Categorical spatial data, such as land cover classes or soil types, are important data sources in many scientific fields, including geography, geology and environment sciences. In geostatistics, indicator kriging (IK) and indicator coKriging (ICK) are typically used for estimating posterior probabilities of class occurrence at any location in space given known class labels at data locations within a neighborhood around that prediction location. In addition, IK and ICK constitute the core of the sequential indicator simulation (SIS) algorithm used for generating realizations of categorical fields. Both IK and ICK require a set of consistently specified indicator (cross)covariance or (cross)variogram models, whose parameter inference can become cumbersome. In addition, IK and ICK may yield estimated probabilities that do not satisfy fundamental probability constraints. To overcome these limitations, transition probability diagrams have been used as an alternative measure of spatial structure for categorical data. More recently, a Spatial Markov Chain (SMC) model was developed for combining transition probabilities into posterior probabilities of class occurrence, under the conditional independence assumption between neighboring data. This paper surveys alternative approaches for combining pre-posterior (two-point) auto- and cross-transition probabilities of class occurrence between any datum location and a prediction or simulation location into conditional or posterior (multi-point) such probabilities. Advantages and disadvantages of existing approaches are highlighted. Last, a proposal is made to synthesize elements of geostatistical and Markov Chain approaches for combining transition probabilities for prediction and simulation of categorical fields.

Keywords: indicator cokriging, transition probability, Markov Chain, geostatistics, spatial statistics

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).