Course detail

Statistical Methods

FAST-HA51Acad. year: 2014/2015

- Programming in Matlab
- Basic notions of the theory of probability and mathematical statistics
- Propagation of errors
- Elipse and elipsoid of errors
- Variance analysis with one factor
- Variance analysis with two factors
- Testing of normality distribution
- Regression analysis
- Some notions of Kalman filtering

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

Ing. Pavel Špaček, Dr.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Students are given basic understanding of the programming in MATLAB language. Principle methods of the theory of probability and statistics are developped and students apply them to some data sets using MATLAB programming. Some topics from numerical mathematics are studied, namely orthogonalization and aproximate solutions of "unsolvable" systems of linear equations. Students should use the letter topic namely in the linear regression theory.

Prerequisites

Basics of the theory of functions of one and several real variables (derivative, partial derivative, limit, continuous functions, graphs of functions, integral). Basic operations with matrices and vectors. Notions randomn variable, basic properties in the theory of probability, notions in the theory of estimation, basics of the theory of testing.

Co-requisites

Programming in Matlab, Maple or Excel

Planned learning activities and teaching methods

LMS Moodle, compiling of Matlab programs to analyse some data sets.

Assesment methods and criteria linked to learning outcomes

Students should not be absent during the course. In case of longer absence, which can be caused by a longer disease, the student should work on additional examples at home. Successful participants of the course should be able to create programs solving different problems discussed in the course. The most significant condition of success in the course is a final written test solved with Matlab programming package.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Give the students a basic understanding of the theory of probability. Students should be able to interpret the basics of mathematical statistics.
Teach the students how to evaluate data focussing on finding solutions to "unsolvable" systems of linear equations with minimum errors.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KOUTKOVÁ, H., MOLL, I.: Úvod do pravděpodobnosti a matematické statistiky. Akademické nakladatelství CERM, s.r.o., 2001. (CS)

Recommended reading

Huaan, Fan: Theory of Errors and Least Squares Adjustment. Royal Institute of Technology, Stockholm, Sweden, 2003. ISBN 91-7170-200-8. (EN)

Classification of course in study plans

  • Programme N-P-C-GK Master's

    branch G , 1 year of study, summer semester, elective

Type of course unit

 

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Pavel Špaček, Dr.

Syllabus

- Basic notions of the theory of probability and mathematical statistics
- Propagation of errors
- Elipse and elipsoid of errors
- Variance analysis with one factor
- Variance analysis with two factors
- Testing of normality distribution
- Regression analysis
- Some notions of Kalman filtering