Stochastic Modelling (FSI-S2M)

Academic year 2018/2019
Supervisor: doc. RNDr. Zdeněk Karpíšek, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The course objective is to make students familiar with selected parts from probability theory and mathematical statistics, which extend students` knowledge acquired in previous courses. In addition other methods for modelling technical processes on PC are introduced.
Learning outcomes and competences:
Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to use PC model and optimize responsible characteristics and properties of technical systems and processes.
Prerequisites:
Methods of mathematical analysis of real and complex functions, probability theory and mathematical statistics.
Course contents:
The following topics are dealt with: characteristic functions of random variables and vectors, functions of random vector and their statistical analyses, multiple normal distribution, fitting of probability distributions by means of classical statistical methods, kernel estimates and quasinorms.
Teaching methods and criteria:
The course is taught through exercises which are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Graded course-unit credit requirements: active participation in seminars, mastering the subject matter, assignments elaboration; evaluation is based on the semester assignment results.
Controlled participation in lessons:
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Type of course unit:
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Exercise Characteristic function of random variable, properties.
Calculating characteristic function of random variables.
Moments of random variables by the help of characteristic function.
Characteristic function of random vector, properties.
Function of random variable and random vector, convolution.
Estimates for function of random variable and random vector.
Multiple normal probability distribution, properties.
Gram - Charlier models A and B.
Pearson curves, Edgeworth and Johnson model.
Kernel estimates of probability density.
Entropy of probability distribution.
Estimates of distribution by the help of minimum Shannon quasinorm.
Estimates of distribution by the help of minimum Hellinger quasinorm.
Literature - fundamental:
1. Gallant, A. R.: Nonlinear Statistical Models. New York : John Wiley, 2003.
2. Silverman, B.W.: Density Estimation for Statistics and Data Analysis. London : Chapman & Hall, 1999.
3. Pitman, E. J. G.: Some Basic Theory for Statistical Inference. New York :John Wiley & Sons, 1978.
5. MONTGOMERY, Douglas C. a George C RUNGER. Applied statistics and probability for engineers. 5th ed. Hoboken: John Wiley, 2011, xv, 768 s. : il. ; 27 cm. ISBN 978-0-470-05304-1.
Literature - recommended:
1. Anděl, J.: Statistické metody. Praha : Matfyzpress, 1993.
2. Potocký, R. a kol.: Zbierka úloh z pravdepodobnosti a matematickej štatistiky. Bratislava/Praha : Alfa/SNTL, 1986.
3. Likeš, J. - Machek, J.: Matematická statistika. Praha : SNTL, 1983.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2A-P full-time study M-MAI Mathematical Engineering -- GCr 3 Elective (voluntary) 2 1 W