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Bayes multiclass classification of spatial Gaussian data following the universal kriging model is considered. The closed-form expressions for the maximum likelihood (ML) estimator of regression parameters and the actual error rate (AER) in terms of semivariograms are derived., Straipsnyje analizuojama erdvinių Gauso duomenų Bajeso klasifikavimo procedūra universalaus krigingo modeliui. Išvestos išreikštinės maksimalaus tikėtinumo regresijos parametrų įverčių išraiškos bei aktualioji (įvertinta) klasifikavimo paklaida, pagrįstos semivariogramomis.

Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.

Bayes multiclass classification of spatial Gaussian data following the universal kriging model is considered. The closed-form expressions for the maximum likelihood (ML) estimator of regression parameters and the actual error rate (AER) in terms of semivariograms are derived.

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.

Straipsnyje analizuojama savarankiško darbo įtaka matematinių kompetencijų ugdymui, apžvelgiami mokslinės literatūros šaltiniai, pateikiama Taikomosios matematikos dalyko savarankiško darbo organizavimo tvarka, užduočių pavyzdžiai ir jų sąsajos su matematinėmis kompetencijomis. Taip pat pristatomi tyrimo, kuriuo siekiama nustatyti, kaip studentai supranta, kokias matematines kompetencijas išsiugdė atlikdami savarankiškus darbus, bei kaip savarankiškų darbų rezultatai daro įtaką galutiniam Taikomosios matematikos egzamino vertinimui, rezultatų analizė. The article describes how important an impact of own-study work skills for development of mathematical competences based on the analysis of the scientific literature. The paper presents organization order of Applied Mathematics own-study work as well as examples of tasks and their links with development of mathematical competences. This article presents a study aimed at determining how students understand which of mathematical competencies developed by doing independent work, as well as the results of individual work influence to the final exam Applied Mathematics assessment, analysis of the results.

Straipsnyje apibūdinama mokymo metodų samprata bei jų skirstymas pagal įvairias mokslininkų metodikas, be to išskiriami inovatyvūs mokymo metodai (IMM), nagrinėjami šių metodų taikymo privalumai ir trūkumai dėstant matematiką. Kolegijų matematikos dėstytojų apklausos rezultatai parodė, kad dažniausiai taikomi tradiciniai mokymo metodai, technologijų ir skirtingų metodikų pagalba integruojant į juos inovatyvius metodus. This paper describes the concept of teaching methods and their distribution to the various scientific methods, in addition to described innovative teaching methods. Considered innovative teaching methods advantages and disadvantages of teaching mathematics, the math topics examples. College mathematics teachers survey showed that the most applied are traditional methods by integrating into them innovative methods, based on technologies and different methodologies.