714-0951/02 – Mathematical statistics and data analysis (MSAD)
Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 10 |
Subject guarantor | Mgr. Marcela Rabasová, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
Study level | postgraduate | Requirement | Choice-compulsory |
Year | | Semester | winter + summer |
| | Study language | Czech |
Year of introduction | 1999/2000 | Year of cancellation | 2012/2013 |
Intended for the faculties | HGF | Intended for study types | Doctoral |
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:
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
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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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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