Course detail

Probability, Statistics and Data Analysis: Introductive Course

FSI-S1D-AAcad. year: 2024/2025

Summary and expansion of elementary concepts from probability theory and mathematical statistics. 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 and categorical data analysis.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Institute of Mathematics (ÚM)

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

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 60 minutes. The evaluation of each test is 0-10 points.

Project evaluation: 0-10 points.

Examination: written and oral. Exam, questions are selected from a list of 4 set areas (25+25+25+25 points). At least a basic knowledge of the terms and their properties is required in each of the areas. Evaluation by points: excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 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 an emphasis on applicability to data.


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
  • correlation analysis
  • regression analysis including regression modeling
  • nonparametric methods
  • creation of parameter estimates
  • Bayesian statistics

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Dobson, A.J., Barnett, A.G. An Introduction to Generalized Linear Models. 4th ed. Chapman & Hall.,2002, ISBN: 978-1138741515 (EN)
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 (EN)
Casella, G., Berger, R.L. Statistical Inference. 2nd ed., 2001. ISBN: 978-0534243128 (EN)
Larsen, R., Marx, M., Introduction to Mathematical Statistics and Its Applications, 6nd ed., 2017. ISBN: 978-01341142178 (EN)

Recommended reading

Montgomery, D, C., Runger G.C. Applied Statistics and Probability for Engineers, 7th Edition, 2018, ISBN: 978-1-119-40036-3 (EN)
ANDĚL, Jiří. Základy matematické statistiky. 3., opr. vyd. Praha: Matfyzpress, 2011. ISBN 978-80-7378-001-2. (CS)

Classification of course in study plans

  • Programme N-LAN-A Master's 1 year of study, winter semester, compulsory-optional

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

  1. Summarizing and recalling the knowledge and methods used in previous courses - probability, random variable.
  2. Summarizing and recalling the knowledge and methods used in previous courses - random vector, mathematical statistics. An outline of other areas of probability and statistics that will be covered.
  3. Extension of hypothesis tests for binomial and normal distributions.
  4. Analysis of variance (simple sorting, ANOVA), post-hoc analysis.
  5. Correlation analysis
  6. Regression analysis - part 1.:linear regression model. Comparison of regression models.
  7. Regression analysis - part 2.:non-linear regression model. 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.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

  1. A reminder of the examples discussed in previous courses - probability, random variable.
  2. A reminder of the examples discussed in previous courses - random vector, mathematical statistics.
  3. Hypothesis tests for binomial and normal distributions.
  4. Project assignment, analysis of variance, post-hoc analysis.
  5. Correlation analysis
  6. Regression analysis – linear models.
  7. Regression analysis – non-linear models.
  8. Distribution tests
  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.