Prediction and simulation in categorical fields: A transition probability combination approach

The investigation of spatial patterns implied in categorical spatial data, such as land use and land cover (LULC) classes and socio-economic statistics data, is involved in many aspects of geographical information science, such as spatial uncertainty modeling and spatial data mining. The discrete nature of categorical fields limits the application of traditional analytical methods, such as kriging-type algorithms, widely used in Gaussian random fields. This paper presents a new probabilistic method for modeling the 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 the proposed method, the conditional or posterior (multi-point) probabilities are approximated by weighted combinations of pre-posterior (two-point) transition probabilities (rather than indicator covariances or vari-ograms) while accounting for spatial interdependencies that most of current approaches often ignore. Using sequential indicator simulation based on the properties of a truncated multi-variate Gaussian field as reference, the advantages and disadvantages of this new proposed approach are analyzed and highlighted.