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

Czech

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Karpíšek, CSc.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Rudiments of the theory probability and mathematical statistics.

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

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.
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

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anderson, T.W.: Statistical Analysis of Time Series. New York : John Wiley & Sons, Inc., 2004.
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

Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : PLUS, 1994.

Classification of course in study plans

  • Programme D-APM-P Doctoral 1 year of study, summer semester, recommended course
  • Programme D-APM-K Doctoral 1 year of study, summer semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus

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.