Course details
Statistics and Probability
MSP Acad. year 2024/2025 Winter semester 6 credits
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, nonparametric methods, categorical data analysis. Markov decisionmaking processes and their analysis, randomized algorithms.
Guarantor
Course coordinator
Language of instruction
Completion
Time span
 26 hrs lectures
 4 hrs seminar
 23 hrs exercises
 16 hrs projects
Assessment points
 60 pts final exam (written part)
 20 pts midterm test (written part)
 20 pts projects
Department
Lecturer
Češka Milan, doc. RNDr., Ph.D. (DITS)
Eryganov Ivan, Ing., Ph.D. (IM DSO)
Hrabec Pavel, Ing., Ph.D. (IM DSO)
Žák Libor, doc. RNDr., Ph.D. (IM DSO)
Instructor
Benko Matej, Ing. (IM)
Češka Milan, doc. RNDr., Ph.D. (DITS)
Eryganov Ivan, Ing., Ph.D. (IM DSO)
Hrabec Pavel, Ing., Ph.D. (IM DSO)
Hudák David, Ing. (DITS)
Macák Filip, Ing. (DITS)
Mrázek Vojtěch, Ing., Ph.D. (DCSY)
Žák Libor, doc. RNDr., Ph.D. (IM DSO)
Learning objectives
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:
 parametric estimation based on known probability distribution
 simultaneous testing of multiple parameters
 goodness of fit tests
 regression analysis including regression modeling
 nonparametric methods
 maximum likelihood estimation
 Markov processes
 randomised algorithms
Prerequisite knowledge and skills
Foundations of differential and integral calculus.
Foundations of descriptive statistics, probability theory and mathematical statistics.
Study literature
 Anděl, Jiří. Základy matematické statistiky. 3., Praha: Matfyzpress, 2011. ISBN 9788073780012.
 FELLER, W.: An Introduction to Probability Theory and its Applications. J. Wiley, New York 1957. ISBN 990000147X
 Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN13: 9780321795434 2013
 Zvára, Karel. Regrese. 1., Praha: Matfyzpress, 2008. ISBN 9788073780418
 Meloun M., Militký J.: Statistické zpracování experimentálních dat (nakladatelství PLUS, 1994).
 D. P. Bertsekas, J. N. Tsitsiklis. Introduction to Probability, Athena, 2008. Scientific
Fundamental literature

DeGroot, Morris H., Schervish, Mark J. Probability and Statistics (4th Edition). Boston: AddisonWesley, 2010. ISBN 03215004661.
Syllabus of lectures
 Summary and recall of knowledge and methods used in the subject of IPT  probability, random variable. Markov processes and their analysis.
 Markov decision processes and their basic analysis.
 Introduction to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).
 Selected probability distributions, conditional probability, likelihood and likelihood function
 Construction of maximum likelihood estimators (MLE), and properties of MLE
 Sufficient statistics, Fisher information and construction of asymptotic confidence intervals
 Probability distribution of sums (averages) of selected random variables, classical construction of confidence intervals and introduction to hypothesis testing
 Linear model, ttest for equal variances, ANOVA
 Posthoc comparisons for ANOVA, test for equal variances, normality test.
 Linear regression model, tests for statistical significance of coefficients and submodels, confidence and prediction intervals for response
 Linear regression model diagnostics.
 Nonparametric hypotheses testing ans tests for categorical data..
 Goodness of fit tests, likelihood ratio test, introduction to generalized linear models.
Syllabus of seminars
 Application of basic statistical methods, statistic a programming.
 Application of advanced statistical methods.
Syllabus of numerical exercises
 Application and analysis of Markov processes.
 Basic application and analysis of Markov decision processes.
 Design and analysis of basic randomised algorithms.
 Condional probability, likelihood function.
 Maximum likelihood estimation.
 Sufficient statistics, Fisher information, asymptotical confidence intervals
 Basic statistical hypothesis testing
 ANOVA
 Posthoc comparisons, tests for equal variances, normality test.
 Computation of linear regression model, tests for statistical significance of its coefficients and submodels.
 Confidence anf prediction intervals for response in linear regression, regression diagnostics.
 Selected nonparametric hypotheses tests, tests for categorical data.
 KolmogorovSmirnov (Liliefors) test, likelihood ratio test.
Syllabus  others, projects and individual work of students
 Basic statistics and programming.
 Usage of tools for solving statistical problems (data processing and interpretation).
Progress assessment
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 10th week focuses on maximum likelihood estimation and basic hypotheses testing.
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: 060 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.
Schedule
Day  Type  Weeks  Room  Start  End  Capacity  Lect.grp  Groups  Info 

Tue  lecture  1., 2., 3. of lectures  E104 E105 E112  10:00  11:50  294  1MIT 2MIT  NBIO  NSPE xx  Češka 
Tue  lecture  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  E104 E105 E112  10:00  11:50  294  1MIT 2MIT  NBIO  NSPE xx  Hrabec 
Tue  exercise  1., 2., 3. of lectures  D0207  12:00  13:50  90  1MIT 2MIT  xx  Češka 
Tue  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  D0207  12:00  13:50  90  1MIT 2MIT  xx  Hrabec 
Tue  seminar  20241008  E104 E105 E112  19:00  20:50  220  1MIT 2MIT  NBIO  NSPE xx  Mrázek 
Tue  seminar  20241126  E104 E105 E112  19:00  20:50  220  1MIT 2MIT  NBIO  NSPE xx  Hrabec 
Wed  exercise  1., 2., 3. of lectures  D0207  08:00  09:50  40  1MIT 2MIT  xx  Macák 
Wed  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  D0207  08:00  09:50  40  1MIT 2MIT  xx  Eryganov 
Wed  exercise  1., 2., 3. of lectures  D0207  10:00  11:50  45  1MIT 2MIT  xx  Macák 
Wed  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  D0207  10:00  11:50  45  1MIT 2MIT  xx  Eryganov 
Thu  exercise  1., 2., 3. of lectures  G202  08:00  09:50  40  1MIT 2MIT  xx  Češka 
Thu  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  G202  08:00  09:50  40  1MIT 2MIT  xx  Hrabec 
Thu  exercise  1., 2., 3. of lectures  G202  10:00  11:50  40  1MIT 2MIT  xx  Češka 
Thu  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  G202  10:00  11:50  40  1MIT 2MIT  xx  Hrabec 
Fri  exercise ^{*)}  20240920  G202  08:00  09:50  3  1MIT 2MIT  xx  Hudák 
Fri  exercise  2., 3. of lectures  G202  10:00  11:50  40  1MIT 2MIT  xx  Andriushchenko 
Fri  exercise  4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures  G202  10:00  11:50  40  1MIT 2MIT  xx  Eryganov 
Fri  exercise  20240920  G202  10:00  11:50  40  1MIT 2MIT  xx  Hudák 
Course inclusion in study plans