M9901 Theory and practice of spline smoothing

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Mgr. Vojtěch Šindlář (seminar tutor)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Wed 10:00–11:50 MP2,01014a
  • Timetable of Seminar Groups:
M9901/01: Tue 16:00–17:50 MP1,01014, V. Šindlář
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main goal of the course is to become familiar with interpolation and smoothing using one-dimensional and multivariate splines, generalised additive models, outlier detection with applications to electrocardiology, electroencephalography, shape analysis (geometrical morphometrics) on biological objects, statistical analyses of multivariate data, testing of multivariate statistical hypotheses, multivariate SVD models (e.g. generalized PCA), 2D/3D statistical visualisation and implementation to R language.
Learning outcomes
Student will be able:
- to understand principles of spline interpolation and smoothing for curves and surfaces;
- to build up and explain suitable model for curves and surfaces;
- to apply spline interpolation and smoothing to real data;
- to implement methods of spline interpolation and smoothing to R.
Syllabus
  • geometric transformations in 2D and 3D,
  • one-dimensional and multivariate splines, generalised additive models and functional models for curves and surfaces in random sample,
  • identification of anatomical landmarks, curves, and surfaces,
  • testing of multivariate statistical hypotheses,
  • multivariate statistical methods for EEG, ECG, and morphometric data,
  • 2D/3D statistical graphics
Literature
    recommended literature
  • JOHNSON, Richard A. and Dean W. WICHERN. Applied multivariate statistical analysis. 3rd ed. Englewood Cliffs: Prentice-Hall, 1992. xiv, 642 s. ISBN 0-13-041807-2. info
    not specified
  • CASELLA, George and Roger L. BERGER. Statistical inference. 2nd ed. Pacific Grove, Calif.: Duxbury, 2002. xxviii, 66. ISBN 0534243126. info
Teaching methods
Lectures 2 hours a week.
Practicals 2 hours a week.
On-line using MS Teams or full-time according to the according to the development of the epidemiological situation and the applicable restrictions.
Assessment methods
Homework, oral exam. The conditions may be specified according to the development of the epidemiological situation and the applicable restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lectures are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The lectures will take place online at MS Teams at the time of the normal lectures according to the schedule. Due to the possible low signal quality, I recommend students not to use the camera. Questions during the lecture will not be possible to ask by voice, but by chat.

The recording from the lecture will be uploaded in the IS sequentially and not in advance, so the recording will be uploaded only after the given lecture and before the next lecture. The recordnig does not have to contain a complete lecture, it is up to a teacher what to share from the record and share it with the students. What is a lecture recording? It can be a PDF of text written by the lecturer on the screen with an electronic pen during the lecture, and this can be supplemented by the voice (or voice and video) of the lecturer. Slides in PDF with TeX-ed text will always be available in the IS and will be shared only after the given lecture and before the next lecture.

Consultations about the lectures will take place through a discussion forum, where the lecturer / instructor moderates this discussion and new discussion forums established by students will not be taken into account. Discussion forums will be based on individual lectures and practicals (if the course has practicals) and about homework. Discussions by e-mail will not take place.

The course is also listed under the following terms Autumn 2011, Spring 2014, Spring 2015, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2021/M9901