Course detail
Dynamic and Multivariate Stochastic Models
FSI-9DVMAcad. year: 2024/2025
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.
Language of instruction
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
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.
Attendance at lectures is not compulsory, but is recommended.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, Inc., 2010.
Hebák, P., Hustopecký, J., Jarošová, E., Pecáková, I.: Vícerozměrné statistické metody 1, 2, 3, Praha: INFORMATORIUM, 2004. (CS)
Ryan, P. R.: Modern Regression Methods. New York : John Wiley & Sons, Inc., 1997.
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.