230-0264/02 – Mathematical Methods in Safety Engineering (MMBI)
| Gurantor department | Department of Mathematics | Credits | 10 |
| Subject guarantor | doc. Ing. Martin Čermák, Ph.D. | Subject version guarantor | doc. Ing. Martin Čermák, Ph.D. |
| Study level | postgraduate | Requirement | Choice-compulsory type B |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FBI | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The course introduces the basics of stochastic data analysis and data modelling on the level required for measurement, datafiles, and time-series processing in the field of Safety and Risk Analysis.
The participant of this course will be able to formulate scope of analysis, which is able to achieve using the given data, choose the suitable model, apply it to given problem including the practical implementation in appropriate software, and present the relevant results of the analysis. Additionally, the participant will learn how to analyse the time-series using the common analysis tools and choose the suitable efficient method for analysis, propose questions and interpret the conclusion learned from data, predict based on optimal model, and assess the model suitability respect to processed data.
Teaching methods
Lectures
Summary
The course introduces the basics of stochastic data analysis and data modelling on the level required for measurement, datafiles, and time-series processing in the field of Safety and Risk Analysis.
The participant of this course will be able to formulate scope of analysis, which is able to achieve using the given data, choose the suitable model, apply it to given problem including the practical implementation in appropriate software, and present the relevant results of the analysis. Additionally, the participant will learn how to analyse the time-series using the common analysis tools and choose the suitable efficient method for analysis, propose questions and interpret the conclusion learned from data, predict based on optimal model, and assess the model suitability respect to processed data.
Compulsory literature:
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
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Tests, semester project, consultations for the subject of dissertation thesis and the publications of the student, oral exams.
E-learning
Other requirements
Tests, semester project, consultations for the subject of dissertation thesis and the publications of the student, oral exams.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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