# 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
Instruction secured by
CER365 doc. Ing. Martin Čermák, Ph.D.
POS220 Ing. Lukáš Pospíšil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 20+0
Part-time Examination 20+0

### 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.

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:

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

### 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.

### 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

Part-time form (validity from: 2021/2022 Winter semester)
Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (P1032D020005) Fire Protection and Safety K English Ostrava Choice-compulsory type B study plan
2024/2025 (P1032D020005) Fire Protection and Safety P English Ostrava Choice-compulsory type B study plan
2023/2024 (P1032D020005) Fire Protection and Safety K English Ostrava Choice-compulsory type B study plan
2023/2024 (P1032D020005) Fire Protection and Safety P English Ostrava Choice-compulsory type B study plan
2022/2023 (P1032D020005) Fire Protection and Safety P English Ostrava Choice-compulsory type B study plan
2022/2023 (P1032D020005) Fire Protection and Safety K English Ostrava Choice-compulsory type B study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

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