Course detail
Statistics and Probability
FIT-MSPAcad. year: 2021/2022
Summary of elementary concepts from probability theory and mathematical statistics. Limit theorems and their applications. Parameter estimate methods and their properties. Scattering analysis including post hoc analysis. Distribution tests, tests of good compliance, regression analysis, regression model diagnostics, non-parametric methods, categorical data analysis. Markov decision-making processes and their analysis, randomized algorithms.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Learning outcomes of the course unit
Students will extend their knowledge of probability and statistics, especially in the following areas:
- Parameter estimates for a specific distribution
- simultaneous testing of multiple parameters
- hypothesis testing on distributions
- regression analysis including regression modeling
- nonparametric methods
- Markov processes
- randomised algorithms
Prerequisites
Foundations of descriptive statistics, probability theory and mathematical statistics.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Three tests will be written during the semester - 6th and 11th week. The exact term will be specified by the lecturer. The test duration is 60 minutes. The evaluation of each test is 0-10 points.
Projected evaluated 0-10 points.
Final written exam - 60 points
Course curriculum
Work placements
Aims
Introduction of further concepts, methods and algorithms of probability theory, descriptive and mathematical statistics. Development of probability and statistical topics from previous courses. Formation of a stochastic way of thinking leading to formulation of mathematical models with emphasis on information fields.
Specification of controlled education, way of implementation and compensation for absences
Participation in lectures in this subject is not controlled
Participation in the exercises is compulsory. During the semester two abstentions are tolerated. Replacement of missed lessons is determined by the leading exercises.
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
D. P. Bertsekas, J. N. Tsitsiklis. Introduction to Probability, Athena, 2008. Scientific
FELLER, W.: An Introduction to Probability Theory and its Applications. J. Wiley, New York 1957. ISBN 99-00-00147-X
Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN-13: 978-0321795434 2013
Meloun M., Militký J.: Statistické zpracování experimentálních dat (nakladatelství PLUS, 1994).
Zvára, Karel. Regrese. 1., Praha: Matfyzpress, 2008. ISBN 978-80-7378-041-8
Classification of course in study plans
- Programme MITAI Master's
specialization NADE , 1 year of study, winter semester, compulsory
specialization NBIO , 1 year of study, winter semester, compulsory
specialization NCPS , 1 year of study, winter semester, compulsory
specialization NEMB , 1 year of study, winter semester, compulsory
specialization NGRI , 1 year of study, winter semester, compulsory
specialization NHPC , 1 year of study, winter semester, compulsory
specialization NIDE , 1 year of study, winter semester, compulsory
specialization NISD , 1 year of study, winter semester, compulsory
specialization NMAL , 1 year of study, winter semester, compulsory
specialization NMAT , 1 year of study, winter semester, compulsory
specialization NNET , 1 year of study, winter semester, compulsory
specialization NSEC , 1 year of study, winter semester, compulsory
specialization NSEN , 1 year of study, winter semester, compulsory
specialization NSPE , 1 year of study, winter semester, compulsory
specialization NVER , 1 year of study, winter semester, compulsory
specialization NVIZ , 1 year of study, winter semester, compulsory
specialization NISY up to 2020/21 , 1 year of study, winter semester, compulsory
specialization NISY , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Summary of basic theory of probability and random variables: axiomatic definition of probability, conditional probability, discrete and continuous random variable, significant probability distributions, random vector.
- Summary of basic methods in statistics: parameter estimate, hypothesis testing, goodness-of-fit tests, regression analysis - regression line.
- Extension of hypothesis tests for binomial and normal distributions.
- Analysis of variance (simple sorting, ANOVA), post hos analysis
- Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.
- Project assignment, demonstration of the use of statistical tools (programs) for solving the project and other statistical tasks.
- Regression analysis. Creating a regression model. Testing hypotheses about regression model parameters. Comparison of regression models. Diagnostics.
- Distribution tests.
- Nonparametric methods of testing statistical hypotheses - part 1.
- Nonparametric methods of testing statistical hypotheses - part 2.
- Markov processes and their analysis.
- Markov decision processes and their basic analysis.
- Introduction to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).
Fundamentals seminar
Teacher / Lecturer
Syllabus
- Summary of basic theory of probability and random variables.
- Summary of basic methods in statistics.
- Hypothesis tests for binomial and normal distributions.
- Analysis of variance, sorting, post host analysis.
- Analysis of categorical data. Contingency table. Four-field tables.
- Demonstration of the use of statistical tools (programs).
- Regression analysis.
- Tests on distribution, tests of good agreement.
- Nonparametric methods of testing statistical hypotheses - one-sample.
- Nonparametric methods of testing statistical hypotheses - two or more sample ones.
- Application and analysis of Markov processes.
- Basic application and analysis of Markov decision processes.
- Design and analysis of basic randomised algorithms.
Project
Teacher / Lecturer
Syllabus
- Usage of tools for solving statistical problems (data processing and interpretation).