Course detail

Statistics and Probability

FIT-MSPAcad. year: 2022/2023

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)

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

Prerequisites

Foundations of differential and integral calculus.

Foundations of descriptive statistics, probability theory and mathematical statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Two tests will be written during the semester - 5th and 10th week. The exact term will be specified by the lecturer. The test duration is 90 minutes. The evaluation of each test is 0-10 points.

Projected evaluated: 0-10 points.

Final written exam: 0-70 points. Students have to achieve at least 30 points, otherwise the exam is assessed by 0 points.

Course curriculum

  1. 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. An outline of other areas of probability and statistics that will be covered.
  5. Extension of hypothesis tests for binomial and normal distributions.
  6. Analysis of variance (simple sorting, ANOVA), post hos analysis.
  7. Regression analysis. Creating a regression model. Testing hypotheses about regression model parameters. Comparison of regression models. Diagnostics.
  8. Distribution tests.
  9. Estimation of parameters using the method of moments and the maximum likelihood method.
  10. Bayesian approach and construction of Bayesian estimates.
  11. Nonparametric methods of testing statistical hypotheses - part 1.
  12. Nonparametric methods of testing statistical hypotheses - part 2
  13. Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.

Work placements

Not applicable.

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

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

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 NISY up to 2020/21 , 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 , 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.
doc. RNDr. Milan Češka, Ph.D.
Ing. Matej Benko
Ing. Pavel Hrabec, Ph.D.

Syllabus

  1. 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. An outline of other areas of probability and statistics that will be covered.
  5. Extension of hypothesis tests for binomial and normal distributions.
  6. Analysis of variance (simple sorting, ANOVA), post hos analysis.
  7. Regression analysis. Creating a regression model. Testing hypotheses about regression model parameters. Comparison of regression models. Diagnostics.
  8. Distribution tests.
  9. Estimation of parameters using the method of moments and the maximum likelihood method.
  10. Bayesian approach and construction of Bayesian estimates.
  11. Nonparametric methods of testing statistical hypotheses - part 1.
  12. Nonparametric methods of testing statistical hypotheses - part 2
  13. Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.

Fundamentals seminar

21 hod., compulsory

Teacher / Lecturer

Ing. Matej Benko
doc. RNDr. Libor Žák, Ph.D.
doc. RNDr. Milan Češka, Ph.D.
Ing. Roman Andriushchenko
Ing. Pavel Hrabec, 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. Hypothesis tests for binomial and normal distributions.
  6. Project assignment, analysis of variance, post host analysis.
  7. Regression analysis.
  8. Tests on distribution, tests of good agreement.
  9. The method of moments and the maximum likelihood method.
  10. Bayesian estimates.
  11. Nonparametric methods of testing statistical hypotheses - part 1.
  12. Nonparametric methods of testing statistical hypotheses - part 2.
  13. Analysis of categorical data. Contingency table. Four-field tables

Project

5 hod., compulsory

Teacher / Lecturer

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

Syllabus

  1.  Usage of tools for solving statistical problems (data processing and interpretation).