Dynamic and Multivariate Stochastic Models (FSI-9DVM)

Academic year 2020/2021
Supervisor: doc. RNDr. Zdeněk Karpíšek, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
The objective of the course is formalization of stochastic thinking of students and their familiarization with modern methods of mathematical statistics and possibilities usage of professional statistical software in research.
Learning outcomes and competences:
Students acquire higher knowledge concerning modern stochastic methods, which enable them to model dynamic and multidimensional technical phenomena and processes by means calculations on PC.
Prerequisites:
Rudiments of the theory probability and mathematical statistics.
Course contents:
The course is intended for the students of doctoral degree programme and it is concerned with the modern stochastic methods (stochastic processes and their processing, multidimensional probability distributions, multidimensional linear and nonlinear regression analysis, correlation analysis, principal components method, factor analysis, discrimination analysis, cluster analysis) for modeling of dynamic and multidimensional problems gained at realization and evaluation of experiments in terms of students research work.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
The exam is in form read report from choice area of statistical methods or else elaboration of written work specialized on solving of concrete problems.
Controlled participation in lessons:
Attendance at lectures is not compulsory, but is recommended.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture Stochastic processes, classification, realization.
Moment characteristics, stationarity, ergodicity.
Markov chains and processes.
Time series analysis (trend, periodicity, randomness, prediction).
Multidimensional probability distributions, multidimensional observations.
Sample distributions, estimation and hypotheses testing.
Multidimensional linear regression analysis, model, diagnostic.
Nonlinear regression analysis, correlation analysis.
Principal components analysis, introduction to factor analysis.
Discrimination analysis, cluster analysis.
Statistical software - properties and option use.
Literature - fundamental:
1. Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, Inc., 2010.
2. Ryan, P. R.: Modern Regression Methods. New York : John Wiley & Sons, Inc., 1997.
3. Anderson, T.W.: Statistical Analysis of Time Series. New York : John Wiley & Sons, Inc., 2004.
Literature - recommended:
2. Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : PLUS, 1994.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D4P-P full-time study D-APM Applied Mathematics -- DrEx 0 Recommended course 3 1 S
D-APM-K combined study --- -- DrEx 0 Recommended course 3 1 S