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Multivariate Statistical Methods, 6 credits
Multivariat statistik, 6 hp
TAMS39
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Martin SingullDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse 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 statisticsIntended 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
| UPG1 | Laboratory work and hand in assignments/project | 2 credits | U, G |
| MUN1 | Oral examination | 4 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Martin SingullCourse website and other links
http://courses.mai.liu.se/GU/TAMS39Education components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Course literature
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
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Laboratory work and hand in assignments/project | 2 credits | U, G |
| MUN1 | Oral examination | 4 credits | U, 3, 4, 5 |
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.
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
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
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X
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X
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MUN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
X
|
X
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X
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MUN1
UPG1
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| 2.2 Experimentation, investigation, and knowledge discovery |
X
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X
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UPG1
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| 2.3 System thinking |
X
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X
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| 2.4 Attitudes, thought, and learning |
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X
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MUN1
UPG1
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| 2.5 Ethics, equity, and other responsibilities |
|
X
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MUN1
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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UPG1
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| 3.2 Communications |
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X
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UPG1
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| 3.3 Communication in foreign languages |
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
X
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X
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X
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UPG1
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
|
X
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X
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UPG1
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