The problem of outlier detection is considered with reference to a piecewise-smooth signal corrupted by background Gaussian noise plus spikes. The problem of estimating the variance of background noise is considered and a robust algorithm which solves the problem in such an environment is suggested. The estimate of variance is essential for an outlier detection algorithm as well as for different algorithms for signal (image) analysis. Our approach to outlier detection is based on a Bayesian probabilistic model. The model enables selection of a set of informative tests for outlier detection. An experimental algorithm based on this approach is tested and its comparison with the median based approach is presented.

The paper addresses the problem of discovering a piecewise-smooth structure of vector response function corrupted by heavy noise. The solution is obtained by dynamic programming algorithm in combination with a probabilistic estimate. The comparison with the approach based on clustering technique, is discussed.>

The concept of probabilistic estimate of clustering (PEC) is introduced. It is based on the examination of an ensemble of clustering problems, in addition to the one given, and the estimation of the probability of obtaining clustering of better quality than that achieved for the given problem. Some properties of PEC and experimental results are presented.>

The problem of how to find the 'best' decision rule in the course of a search with the help of analysis of sample set is considered. Specifically the problem of selecting of best subset of regressors is highlighted. The concepts of predictive probabilistic estimate (PPE), decomposition of a search process on stages, ensemble of noise functions and reference probability distribution on it are introduced and discussed. A Monte Carlo procedure for estimating PPE is suggested and applied to a practical example. A method of obtaining upper and lower bounds for the PPE is suggested.>

The influence of sample set structure on decision rule quality for the case of a linear discriminant function is considered. Specifically, the case of missing data in the sample set and the case when the multivariate random variable is to be registered with the help of a single-channel device are investigated. Some rather unusual phenomena are discussed, such as when some new samples are added to the sample set, and as a result the quality of parameter estimations used in a decision rule become better, but at the same time the quality of the decision rule itself becomes worse. The investigation is performed for the classical model of a twocategory classifier when the categories are described by the multivariate normal densities having common covariance matrices. Some results of statistical simulation experiments are included.