| TAMS39 |
Multivariate Statistical Methods, 6 ECTS credits.
/Multivariat statistik/
For:
BME
D
I
II
MED
MMAT
Y
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra, Calculus of Several Variables, a course in probability, a course in statistics
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
The teaching consists of 12 2 hour lectures, 9 2 hour tutorial sessions and 3 2 hour computer lessons.
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Course contents:
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.
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Course literature:
â?~Applied Multivariate Statistical Analysisâ?T, Richard A. Johnson och Dean W. Wichern, Pearson International.
'Methods of Multivariate Statistics', Muni S. Srivastava, Wiley Series in Probability and Statistics
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Examination: |
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Oral examination
Hand in assignments/project
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4 ECTS
2 ECTS
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Course language is English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Martin Singull
Link to the course homepage at the department
Course Syllabus in Swedish
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