Modeling Categorical Random Fields via Linear Bayesian Updating

Abstract: Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.