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Main menu for Browse IS/STAG
Course info
KMA / VSM
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Course description
Department/Unit / Abbreviation
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KMA
/
VSM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Selected Statistical Methods
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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Extended statistical methods, oriented to some applications. Parameter estimation, hypothesis testing, non-parametric and Bayesian methods, quality assurance (control), acceptance sampling, control charts.
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Requirements on student
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Knowledge and abilities assessed: All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of results, procedures and specific problems related to statistic inference.
Assessment criteria: The main criteria for marking will be clear and logical formulation of solution methods and correctness of obtained results.
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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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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Montgomery, Douglas C. Introduction to statistical quality control. Hoboken : John Wiley & Sons, 2005. ISBN 0-471-65631-3.
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Recommended:
Rao, Radhakrishna Calyampudi. Lineární metody statistické indukce a jejich aplikace. Praha : Academia, 1978.
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Recommended:
Blatná, Dagmar. Neparametrické metody. Testy založené na pořádkových a pořadových statistikách.. Praha, Skripta VŠSE, 1996.
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Recommended:
Machek, J. Teorie odhadu. SPN Praha, 1974.
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Recommended:
Rényi, Alfréd. Teorie pravděpodobnosti. 1. české vyd. Praha : Academia, 1972.
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Recommended:
Hátle, Jaroslav; Likeš, Jiří. Základy počtu pravděpodobnosti a matematické statistiky. Praha : SNTL, 1974.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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55
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Contact hours
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56
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Individual project (40)
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35
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Total
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146
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
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) |
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) |
formulate and explain the definition of probability (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) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
apply analytical and mathematical methods to simple time series modeling tasks |
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 |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
define and explain basic terms and principles of non-parametric and Bayesian methods |
define and explain different types of convergence in probability theory |
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. |
explain the definition of the exponential family of distributions and know different examples of distributions falling into this group |
know the basic statistical methods used in the field of statistical quality control |
Skills - skills resulting from the course: |
clearly and logically formulate and defend the chosen solution procedures |
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 |
interpret the outputs of methods and models and explain the obtained results to experts and laymen |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Practical exam |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture with visual aids |
Interactive lecture |
Self-study of literature |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Task-based study method |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
Self-study of literature |
Individual study |
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