Dynamic and Multivariate Stochastic Models
FSI-9DVMAcad. year: 2020/2021
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.
Learning outcomes of the course unit
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.
Rudiments of the theory probability and mathematical statistics.
Recommended optional programme components
Recommended or required reading
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, Inc., 1996.
Hebák, P. - Hustopecký, J.: Vícerozměrné statistické metody. Praha : SNTL/ALFA, 1987.
Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : PLUS, 1994.
Ryan, P. R.: Modern Regression Methods. New York : John Wiley & Sons, Inc., 1997.
Cipra, T.: Analýza časových řad s aplikacemi v ekonomii. Praha : SNTL, 1976.
Anderson, T.W.: Statistical Analysis of Time Series. New York : John Wiley & Sons, Inc., 1994.
Planned learning activities and teaching methods
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.
Language of instruction
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.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not compulsory, but is recommended.
Type of course unit
20 hours, optionally
Teacher / Lecturer
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.
eLearning: opened course