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We consider classification of the realization of a multivariate spatial–temporal Gaussian random field into one of two populations with different regression mean models and factorized covariance matrices. Unknown means and common feature vector covariance matrix are estimated from training samples with observations correlated in space and time, assuming spatial–temporal correlations to be known. We present the first-order asymptotic expansion of the expected error rate associated with a linear plug-in discriminant function. Our results are applied to ecological data collected from the Lithuanian Economic Zone in the Baltic Sea.

This paper deals with the problem of classifying an observation into one of two curved exponential populations. The plug-in classification rule obtained by replacing unknown parameters with their bias-adjusted ML estimators in Bayes classification rule is used. The second-order asymptotic expansion with respect to the inverses of the training sample sizes for the expected regret risk is derived.

The subjects of this research are the surface layer hydrophysical parameters and their spatial-temporal statistical models in the south-eastern Baltic Sea. Here we analyze sea surface water temperature (SST), water salinity and ice phenomena data collected in the period 2009-2012. The Center of Marine Research in Klaipeda (Lithuania) provides us with the data. The purpose of this research is to construct optimal parametric spatial trend and spatial variation (semivariogram) models at different time layers. To use constructed models for ice formation statistical dependence on water salinity and temperature research, also to interpolate and to predict using different linear prediction models (kriging).

The problem of classifying a scalar Gaussian random field observation into one of two populations specified by different parametric drift and common covariance models is considered. The unknown drift and scale parameters are estimated from given spatial training sample. This paper concerns with classification procedures associated with a parametric plug-in Bayes Rule obtained by substituting unknown parameters in the Bayes rule by their estimators. For the particular prior distributions of unknown parameters the Bayesian estimators are used. The closed form expression for the actual risk associated with aforementioned classification rule is derived. Estimator of expected risk is based on derived actual risk and used as performance measure for classifier incurred by plug-in Bayes rule. Stationary Gaussian random field with exponential covariance function sampled on regular 2-dimensional lattice is used for simulation experiment. Critical comparison of the performance of the plug-in Bayes Rule defined above with one based on ML estimators is performed.

Given training sample, the problem of classifying Gaussian spatial data into one of two populations specified by conditional autoregressive model (CAR) with different mean functions is considered. This paper concerns with classification procedures associated with Bayes Discriminant Function (BDF) under deterministic spatial sampling design. In the case of complete parametric certainty, the overall misclassification probability associated with aforementioned BDF is derived. This is the extension of the previous one to the CAR case. Spatial weights based on inverse of Euclidean distance and the second and third order neighbourhood schemes on regular 2-dimensional lattice are used for illustrative examples. The effect of the spatial sampling design, Mahalanobis distances and prior probabilities on the performance of proposed classification procedure is numerically evaluated.

In image classification often occur such situations, when images in some level are corrupted by additive noise. Such noise in image classification can be modeled by Gaussian random fields (GRF). In image classification supervised and unsupervised methods are used. In this paper we compare our proposed supervised classification methods based on plugin Bayes discriminant functions (PBDF) (see [6] and [11]) with unsupervised classification method based on grey level co-occurrence matrix (GLCM) (see e.g. [8] and [1]). The remotely sensed image is used for classification (USGS Earth Explorer). Also GRF with different spatial correlation range are generated and added to the original remotely sensed image. Such situation can naturally occur during forest fire, when smoke covers some territory. These images are used for classification accuracy examination.

In statistical image classification it is usually assumed that feature observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field (GRF) model for features observations. Conditional distribution of label of observation to be classified is assumed to be dependent on its spatial adjacency with training sample spatial framework. Perfomance of the Bayes discriminant function (BDF) and performance of plug-in BDFare tested and are compared with ones ignoring spatial correlation among feature observations.For illustration image of figure corrupted by additive GRF is analyzed. Advantage of proposed BDF against competing ones is shown visually and numerically.

In spatial classification it is usually assumed that features observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field model for features observations. The label are assumed to follow Disrete Random Field (DRF) model. Formula for exact error rate based on Bayes discriminant function (BDF) is derived. In the case of partial parametric uncertainty (mean parameters and variance are unknown), the approximation of the expected error rate associated with plug-in BDF is also derived. The dependence of considered error rates on the values of range and clustering parameters is investigated numerically for training locations being second-order neighbors to location of observation to be classified.

Paper deals with a problem of testing isotropy against geometric anisotropy for Gaussian spatial data. The original simple test statistic based on directional empirical semivariograms is proposed. Under the assumption of independence of the classical semivariogram estimators and for increasing domain asymptotics, the distribution of test statistics is approximated by chi-squared distribution. The simulation experiments demonstrate the efficacy of the proposed test.