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Mathematical Methods in Safety Engineering

Type of study Doctoral
Language of instruction Czech
Code 230-0264/01
Abbreviation MMBI
Course title Mathematical Methods in Safety Engineering
Credits 10
Coordinating department Department of Mathematics
Course coordinator doc. Ing. Martin Čermák, Ph.D.

Osnova předmětu

The introduction to statistics and data processing
Optimization methods: unconstrained problems, problems with equality and inequality constraints
Data processing software: R, Matlab, Excel, Python
Regression models (linear, polynomial, non-linear, autoregression), regularization
Multicriterial optimization
Bayesian inference methods, Markov chains
Spectral analysis: Principal Component Analysis, eigenvalue and singular decompositions
Clustering: K-means, spectral clustering
Time-series: introduction, graphical analysis, descriptive analysis, measures of dynamism
Model suitability analysis, introduction to theory of information

E-learning

Povinná literatura

BRIŠ, R. Probability and statistics for engineers. VŠB-TU Ostrava, 2011. https://homel.vsb.cz/~bri10/Teaching/Prob%20&%20Stat.pdf
SHUMWAY, R. H., STOFFER, D. S. Time Series Analysis and Its Applications: With R Examples. Springer, 4th ed. 2017. ISBN10 3319524518 

Doporučená literatura

ŠKŇOUŘILOVÁ, P., BRIŠ, R. Statistics I, VŠB-TU Ostrava, Ostrava 2007. http://mdg.vsb.cz/portal/en/Statistics1.pdf
MARTINEZ, W. L. Exploratory data analysis with MATLAB. Boca Raton, Fla.: Champman&Hall/CRC, c2005. ISBN 1-58488-366-9 
KANTZ, H., SCHREIBER, T. Nonlinear Time Series Analysis, Cambridge University Press. 2nd ed. 2004. ISBN10 0521529026