Classification risk of Gaussian spatial data using linear discriminant functions

The thesis is devoted to the linear discriminant analysis of spatially correlated data. The presence of spatial correlation violates the assumption of independent observations which is the background for many classical statistical methods. Therefore, when modelling spatial data it is important to incorporate the spatial correlation, as ignoring it may affect the accuracy of classification procedures. The thesis presents the original discriminant functions based on a plug-in Bayes classification rule, taking into account the spatial correlation between the Gaussian observations. The proposed discriminant functions are applied to assign a single Gaussian random field observation to one of several prescribed populations and to assess the classification risk or error rates. The cases of univariate and multivariate Gaussian random fields are explored. The simulation study confirms that the proposed clasifiers are of a good accuracy and also shows that including spatial correlation gives lower classification risk or error rate