Czech

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A student will manage both theoretical and practical knowledge of mathematical statistics and its application in the evaluation of experimental data. He will be able of testing statistical hypotheses, application of regression models and application of more advanced multivariate statistical methods in biomedicine, living environment research, analytical chemistry and and other scientific branches.

Foundations of mathematical analysis and linear algebra. Foundations of the probability theory and the most common continuous and discrete distributions.

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Lecture.

The classification is given by the examination consisting of the test and oral parts.

1. Foundations of descriptive statistics, Point and interval estimations and their properties.
2. Interval estimations, testing of statistical hypotheses, one sample tests, godness of fit tests.
3. Random vectors, simultaneous and marginal distributions, the conditional density and probablistic functions.
4. Numerical characteristics - the concepts of mean value, variance, covariance and correlation matrices. Multivariate normal distribution.
5. Two sample tests. The least square method and linear regression model, applications.
6. Some generalizations and modifications of the linear regression model, intriduction to the non-linear regression, elements of regression diagnostics.
7. Introduction to the variance analysis - the methods of Tuckey, Bartlett´s test, one and two factor ANOVA tests.
8. The method of Schéffe and its application for determining of confidence zone in the linear regression model. Non-parametric tests - the sign test, Wilcoxon's test and Kruskal- Wallis test. 9. Eigen-values and eigen-vectors, the principal component analysis and its application for data reduction.
10. Foundations of factor analysis and its applications in the living environment research.
11. Introduction to the discriminant analysis and its applications in biomedicine. Introduction to the theory of neural nets - inner potential, organization, active and adaptive dynamics.
12. Perceptron nets and the backpropagation method as a fundamental training method. Logistic regression and its connection with perceptrons, applications in biomedicine.
13. Neural nets as an alternative model to the classical statistics data processing. Information about linear associative nets, hebbian training and its applications in informatics (autoassociative and hetero associative memories).

Not applicable.

The aim of the course is to manage and apply the methods of mathematical staistings for processing of experimental data.

Participation on lectures is not compulsory. The course is finished by an examination consisting of the test and oral parts.

Not applicable.

Not applicable.

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Not applicable.