714-0951/02 – Mathematical statistics and data analysis (MSAD)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorMgr. Marcela Rabasová, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1999/2000Year of cancellation2012/2013
Intended for the facultiesHGFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Part-time Credit and Examination 0+0

Subject aims expressed by acquired skills and competences

The aim of the course is to provide theoretical and practical foundation for understanding the importance of basic probability concepts and teach the student statistical thinking as a way of understanding the processes and events around us and to acquaint him with the basic methods of gathering and analyzing statistical data.

Teaching methods

Individual consultations
Project work

Summary

1. Descriptive statistics - statistical file with one factor, statistical file with two factors, grouped frequency distribution 2. Inductive statistics - random sample, point and interval estimations of parameters, hypothesis testing 3. Regression analysis - least squares approximation, linear regression, nonlinear regression

Compulsory literature:

Dummer R. M.: INTRODUCTION TO STATISTICAL SCIENCE. VŠB-TU Ostrava 1998; ISBN 80-7078-497-0

Recommended literature:

Radim Briš, Petra Škňouřilová. STATISTICS I. VŠB - Technical University of Ostrava, Ostrava 2007.

Way of continuous check of knowledge in the course of semester

Tests and credits ================= Teaching is based on individual consultations. Program and the exam questions are analogous to the program of lectures.

E-learning

Other requirements

Requirements are given by the outline of the subject.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1st Approximation methods: Formulation of problems and types of approximations. Polynomial interpolation. Interpolation using B-splines, beta-splines and ni-splines. Shape properties: the non-negativity, convexity and monotonicity. 2nd Approximation of curves and surfaces: Ferguson, Bezier and Coons curves. Interpolation for surfaces using meshesand edges. Cladding. 3rd Fourier transform and its application: continuous and discrete Fourier transform. FFT algorithm. Windowed transform, time-frequency analysis. 4th Wavelet transform: interpretation. Wavelets as function. Multiresolution analysis. Wavelet spaces. Calculations with wavelets. 5th Application 1: Smoothing algorithms based on Fourier transform and on minimizing properties of splines. Data compression. 6th Application 2: The numerical solution of differential equations using splines and wavelets. Shape properties of solutions. 7th Application 3: Algorithms for solving linear systems based on Fourier and wavelet transforms.

Conditions for subject completion

Part-time form (validity from: 1999/2000 Winter semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 0  0
        Examination Examination 100  51
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2012/2013 (P3646) Geodesy and Cartography (3646V001) Mine Surveying and Geodesy K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner