TAMS26 Multivariate Statistical Methods 2010

Study Guide@lith

Valid for year : 2010

TAMS26	Multivariate Statistical Methods, 6 ECTS credits. /Multivariat analys/ For: BME D I Ii MMAT Y
	Prel. scheduled hours: 48 Rec. self-study hours: 112
	Area of Education: Science Main field of studies: Mathematics, Applied Mathematics
	Advancement level (G1, G2, A): A
	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.
	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.
	Organisation: The teaching consists of 12 2 hour lectures, 9 2 hour tutorial sessions and 3 2 hour computer lessons.
	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.
	Course literature: A compendium is available in the bookshop, containing the lecture notes, examples and computer assignments. For further reading, the recommended text is �?~Applied Multivariate Statistical Analysis�?T (latest edition) by Richard A. Johnson and Dean W. Wichern, published by Pearson.
	Examination:
	Written examination Laboratory work and hand in assignments/project	4 ECTS 2 ECTS


Course language is English. Department offering the course: MAI. Director of Studies: Torbjörn Larsson Examiner: John Noble Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 11/02/2010