Course detail

Statistics and Probability

FIT-MSPAcad. year: 2023/2024

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

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Dept. of Statistics and Optimization (ÚM OSO)

Entry knowledge

Foundations of differential and integral calculus.

Foundations of descriptive statistics, probability theory and mathematical statistics.

Rules for evaluation and completion of the course

The evaluation of the course consists of the test in the 5th week (max. 10 points) and the test in the 10th week (max. 10 points), the two projects (max 8 + 12 points), and the final exam (max 60 points).

The written test in the 5th week focuses on Markov processes and on basic randomized algorithms. The written test in the 9th week focuses on advance topics in statistics (will be clarified later).

Projects:

1st project: 8 points (2 points minimum) -- Statistics and programming.
2nd project: 12 points (4 points minimum) -- Advanced statistics.

The requirements to obtain the accreditation that is required for the final exam: The minimal total score of 20 points achieved from the projects and from the tests in the 5th and 10th week (i.e. out of 40 points).

The final written exam: 0-60 points. Students have to achieve at least 25 points, otherwise the exam is assessed by 0 points.

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.

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.

 

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
  • creation of parameter estimates
  • Bayesian statistics
  • Markov processes
  • randomised algorithms 

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ANDĚL, Jiří. Základy matematické statistiky. 3., opr. vyd. Praha: Matfyzpress, 2011. ISBN 978-80-7378-001-2. (CS)

Recommended reading

Anděl, Jiří. Základy matematické statistiky. 3.,  Praha: Matfyzpress, 2011. ISBN 978-80-7378-001-2.
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

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme MITAI Master's

    specialization NSPE , 1 year of study, winter semester, compulsory
    specialization NBIO , 1 year of study, winter semester, compulsory
    specialization NSEN , 1 year of study, winter semester, compulsory
    specialization NVIZ , 1 year of study, winter semester, compulsory
    specialization NGRI , 1 year of study, winter semester, compulsory
    specialization NADE , 1 year of study, winter semester, compulsory
    specialization NISD , 1 year of study, winter semester, compulsory
    specialization NMAT , 1 year of study, winter semester, compulsory
    specialization NSEC , 1 year of study, winter semester, compulsory
    specialization NISY up to 2020/21 , 1 year of study, winter semester, compulsory
    specialization NCPS , 1 year of study, winter semester, compulsory
    specialization NHPC , 1 year of study, winter semester, compulsory
    specialization NNET , 1 year of study, winter semester, compulsory
    specialization NMAL , 1 year of study, winter semester, compulsory
    specialization NVER , 1 year of study, winter semester, compulsory
    specialization NIDE , 1 year of study, winter semester, compulsory
    specialization NEMB , 1 year of study, winter semester, compulsory
    specialization NISY , 1 year of study, winter semester, compulsory
    specialization NEMB up to 2021/22 , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.
Ing. Pavel Hrabec, Ph.D.
Ing. Matej Benko
doc. RNDr. Milan Češka, Ph.D.

Syllabus

  1. Summary and recall of knowledge and methods used in the subject of IPT - probability, random variable. Markov processes and their analysis.
  2. Markov decision processes and their basic analysis.
  3. Introduction to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).
  4. Summary and recall of knowledge and methods used in the subject of IPT (estimates, statistical tests). An outline of other areas of probability and statistics that will be covered.
  5. Estimation of parameters using the method of moments and the maximum likelihood method.
  6. Bayesian approach and construction of Bayesian estimates.
  7. Extension of hypothesis tests for binomial and normal distributions.
  8. Analysis of variance (simple sorting, ANOVA), post hos analysis.
  9. Distribution tests.
  10. Nonparametric methods of testing statistical hypotheses.
  11. Regression analysis. Linear regression models. Testing hypotheses about regression model parameters.
  12. Regression analysis. Comparison of regression models. Diagnostics. Nonlinear regression models.
  13. Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.

Fundamentals seminar

23 hod., compulsory

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.
doc. RNDr. Milan Češka, Ph.D.
Ing. Pavel Hrabec, Ph.D.
Ing. Filip Macák
Ing. Matej Benko
Ing. Roman Andriushchenko
Ing. Ivan Eryganov, Ph.D.

Syllabus

  1. Application and analysis of Markov processes.
  2. Basic application and analysis of Markov decision processes.
  3. Design and analysis of basic randomised algorithms.
  4. Reminder of discussed examples in the IPT subjekt
  5. The method of moments and the maximum likelihood method.
  6. Bayesian estimates.
  7. Hypothesis tests for binomial and normal distributions.
  8. Analysis of variance, post host analysis.
  9. Tests on distribution, tests of good agreement.
  10. Nonparametric methods of testing statistical hypotheses - part 1.
  11. Regression analysis – linear regression models
  12. Regression analysis – diagnostics, non-linear regression models
  13. Analysis of categorical data. Contingency table. Four-field tables

Project

16 hod., compulsory

Teacher / Lecturer

Ing. Pavel Hrabec, Ph.D.
Ing. Matej Benko

Syllabus

  1. Basic statistics and programming. 
  2. Usage of tools for solving statistical problems (data processing and interpretation).

Seminar

4 hod., optionally

Teacher / Lecturer

doc. RNDr. Milan Češka, Ph.D.
Ing. Vojtěch Mrázek, Ph.D.
Ing. Pavel Hrabec, Ph.D.

Syllabus

  1. Application of basic statistical methods, statistic a programming.
  2. Application of advanced statistical methods.

Elearning

eLearning: currently opened course