Multivariate Statistical Methods, 6 credits (TAMS39)

Multivariat statistik, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

Second cycle

Course type

Programme course

Examiner

Martin Singull

Director of studies or equivalent

Ingegerd Skoglund
Course offered for Semester Period Timetable module Language Campus VOF
6CDDD Computer Science and Engineering, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CDDD Computer Science and Engineering, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CMED 9 (Autumn 2017) 1 4 English Linköping v
6CMED (Biomedical Modelling) 9 (Autumn 2017) 1 4 English Linköping v
6CMED (Biomedical Imaging and Visualization) 9 (Autumn 2017) 1 4 English Linköping v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIII Industrial Engineering and Management, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6MBME Biomedical Engineering, Master's programme 3 (Autumn 2017) 1 4 English Linköping v
6MMAT Mathematics, Master's programme 3 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 9 (Autumn 2017) 1 4 English Linköping v
6CITE Information Technology, M Sc in Engineering (Biomedical Engineering) 9 (Autumn 2017) 1 4 English Linköping v

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Computer Science and Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering
  • Industrial Engineering and Management - International, M Sc in Engineering
  • Biomedical Engineering, Master's programme
  • Mathematics, Master's programme
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Information Technology, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Linear Algebra, Calculus of Several Variables, a course in probability, a course in statistics

Intended learning outcomes

This course provides an introduction to multivariate statistical analysis, both theory and methods. The theory discusses multivariate sampling distributions and their characteristic functions, quadratic forms, elliptical distributions, exterior forms, the Wishart distribution and its applications in sampling. The practical side of the course discusses multivariate significance tests, principal component analysis, factor analysis, multivariate distance measures, discriminant analysis, cluster analysis and canonical correlation analysis. These are implemented using appropriate statistical software to analyse data, interpret the results and draw appropriate conclusions. After completing the course the student should be able to:

  • Compute the characteristic functions of some well known distributions and use multivariate characteristic functions to investigate properties of various distributions.
  • Derive various multivariate sampling distributions and use exterior forms where appropriate to make the necessary changes of variables.
  • Understand and be able to use Kronecker products in problems related to the multivariate normal distribution.
  • Understand how the Wishart distribution arises in multivariate sampling and how to use it.
  • Understand how to use various multivariate statistical methods (for example: test for significant differences between populations, use principal component analysis and factor analysis, discriminant analysis, cluster analysis and canonical correlation analysis)
  • Understand the limitations of these multivariate analysis methods.
  • Implement these methods using an appropriate statistical software package and draw appropriate conclusions.

Course content

Results from Linear Algebra. The characteristic function, the multivariate normal distribution and some properties. Generalised inverses. The Euler Gamma function, the chi squared, F and t distributions. Quadratic forms. Spherical and Elliptical Distributions, multivariate cumulants, skewness, kurtosis. Kronecker products, the Multivariate Gamma function, exterior products. Sampling from a multivariate normal distribution, the Wishart distribution and applications. Inferences about mean vectors. Principal components analysis, factor analysis, discriminant analysis and cluster analysis. Canonical correlation. Other multivariate methods. Use of statistical software.

Teaching and working methods

The teaching consists of 12 2 hour lectures, 9 2 hour tutorial sessions and 3 2 hour computer lessons.

Examination

MUN1Oral examinationU, 3, 4, 54 credits
UPG1Laboratory work and hand in assignments/projectU, G2 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Martin Singull

Course website and other links

http://courses.mai.liu.se/GU/TAMS39

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Course literature

Additional literature

Books
Muni S. Srivastava, Methods of Multivariate Statistics Wiley

Wiley Series in Probability and StatisticsRichard A. Johnson och Dean W. Wichern, Applied Multivariate Statistical Analysis Pearson International

Additional literature

Books

Muni S. Srivastava, Methods of Multivariate Statistics Wiley

Wiley Series in Probability and Statistics

Richard A. Johnson och Dean W. Wichern, Applied Multivariate Statistical Analysis Pearson International
MUN1 Oral examination U, 3, 4, 5 4 credits
UPG1 Laboratory work and hand in assignments/project U, G 2 credits

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page. There are no files available for this course.

Page responsible: Info Centre, infocenter@liu.se