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.
In more details:

1. Students manage the probablity theory and elementary methods of one-variate mathematical statistics on the level of point and interval estimations and tests of statistical hypotheses inbothl cases of normal and other distributions including testing of the kind of distribution.
2. Students obtain the skills in the analysis of variance - particularly in one-way and two-way ANOVA methods, Bartlett test, the methods by Tuckey and Shéffe. They make acquaintance with applications of such methods. Students will be able to verify the regularity of the application of ANOVA, or they or select another method, e.g. Kruskal-Wallis test.
3. Students manage linear regression and foundations of non-linear regression both theoratically and computationally, including interval estimations and tests of hypotheses over regression coefficients. Given a practical problem, they will be able to evaluate the adequacy of the application of the regression model.
4. Students make acquaintance with the multivariate normal distribution and the related distributions. They manage the point and interval estimations of parameters of multivariate normal distribution and tests of hypotheses on them.
5. Students manage the principal component method. They comprehend its meaning for the reduction of input parameters and its applications.
6. Students make acquaintance with the elements of the factor and discriminant analysis.
7. Students make acquaintance with the elements with the foundations of the theory of neural nets and with its possible application as an alternative to methods of classical statistics.
They manage the back-propagation alghoritm and some elementary kinds of neural nets and its applications.

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. Both parts of the examinations form 50 percent of the total marking.

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. Multivariate normal distribution - point and interval estimations on parameters of multivariate normal distribution, tests of hypotheses over them.
6. The least square method and linear regression model, applications. Interval estimations and test of hypotheses over the regression coefficients. Some generalizations and modifications of the linear regression model, introduction 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 a test (50% of marking) and an oral part (50% of marking) .

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