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Lecturer(s)
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Course content
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1. Convergence of random variables. Convergence in distribution, in probability, almost sure convergence, in the k-th mean, examples. 2. Point estimators, exponential family of distributions, Cramér-Rao lower bound, Fisher information. Some information theory methods, Bayesian estimations. 3. Confidence intervals, advanced construction methods. Statistical tolerance limits, definition and estimation's methods. 4. Tolerance and prediction areas, continuous random variables, Wilk's tolerance limits. Large sample tolerance limits. Tolerance limits in the case discrete probability distributions. 5. Ratio statistics, large sample case. Small sample case. Cauchy and Pareto distributions. Fat tails and its statistical consequences. 6. Rank statistics. Spearman's correlation, Kendal tau, introduction to copulaes. Stochastic order and dominance. 7. Hypothesis testing - advanced methods, sequential tests, multiple sampling tests, independency hypothesis testing. 8. Sampling by measuring. 9. Acceptance sampling. 10. Control charts, order statistics, max and min distribution, sample range distribution. 11. X-R, X-S charts in normal distribution case, in the some others distribution. Modification for discrete and categorical variables. 12. Kernel probability density estimators, non-parametric regression, heteroskedasticity and skedastic function. Some kernels and bandwidth parameter determination.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Lecture with practical applications, One-to-One tutorial
- Preparation for an examination (30-60)
- 55 hours per semester
- Individual project (40)
- 35 hours per semester
- Contact hours
- 56 hours per semester
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| prerequisite |
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| Knowledge |
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| describe and explain the principles of statistical inference - especially the principles of point and interval estimates and the principles of statistical hypothesis testing (within the scope of the KMA/PSA subject) |
| to know the various attitudes to statistical time series modeling (within the scope of the KMA/SA2 subject) |
| formulate and explain the definition of probability (within the scope of the KMA/PSA subject) |
| describe and explain different types of distribution of random variables, know their basic properties and possibilities of use (within the scope of the subject KMA/SA1) |
| Skills |
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| distinguish betwwen different types of random variables (discrete, continuous) and different types of distribution |
| use knowledge of basic statistical methods and procedures for simple data analysis |
| apply analytical and mathematical methods to simple time series modeling tasks |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| define and explain the terms and principles of advanced statistical methods, especially more general methods of constructing interval estimates, more general methods of testing statistical hypotheses, etc. |
| define and explain different types of convergence in probability theory |
| define and explain basic terms and principles of non-parametric and Bayesian methods |
| know the basic statistical methods used in the field of statistical quality control |
| explain the definition of the exponential family of distributions and know different examples of distributions falling into this group |
| Skills |
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| clearly and logically formulate and defend the chosen solution procedures |
| interpret the outputs of methods and models and explain the obtained results to experts and laymen |
| correctly apply the formal and content side in mathematical expression, both written and oral |
| choose appropriate methods for analyzing a given real problem and assess the relevance of their assumptions |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture with visual aids |
| Interactive lecture |
| Self-study of literature |
| Skills |
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| Practicum |
| Task-based study method |
| Individual study |
| Competences |
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| Lecture |
| Practicum |
| Self-study of literature |
| Individual study |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Skills |
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| Practical exam |
| Competences |
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| Oral exam |
| Written exam |
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Recommended literature
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Blatná, Dagmar. Neparametrické metody. Testy založené na pořádkových a pořadových statistikách.. Praha, Skripta VŠSE, 1996.
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Hátle, Jaroslav; Likeš, Jiří. Základy počtu pravděpodobnosti a matematické statistiky. Praha : SNTL, 1974.
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Machek, J. Teorie odhadu. SPN Praha, 1974.
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Montgomery, Douglas C. Introduction to statistical quality control. Hoboken : John Wiley & Sons, 2005. ISBN 0-471-65631-3.
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Rao, Radhakrishna Calyampudi. Lineární metody statistické indukce a jejich aplikace. Praha : Academia, 1978.
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Rényi, Alfréd. Teorie pravděpodobnosti. 1. české vyd. Praha : Academia, 1972.
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