Multivariate Statistics

• Explain structure of multivariate data, and calculate the structure of linear combinations of such data
• Apply the multivariate normal distribution to describe multivariate data, and assess it’s relevance in a given case
• Identify relevant distributions derived from the normal distribution, and apply those in conclusions of performed analyses
• Interpret multivariate data based on eigenvalue analyses of correlation- and variance-covariance-structures
• Construct relevant models with both univariate and multivariate respons variables, and evaluate the model quality in a given case
• Suggest an analysis for a given set of data, and find the parameters and other relevant quantities
• Able to use the statistical software packages SAS or R, including identifying relevant quantities in and interpreting output from this package.
• Relate formulas and concepts from the course with the relevant quantities in SAS or R

We will cover a large fraction of the following multidimensional models: Multidimensional distributions, multiple and partial correlation. The general linear model: Estimation and testing, geometric interpretation. Regression analysis: Estimation and testing, determination of best regression equations, analysis of residuals, prediction intervals, non-linear analysis etc. Multidimensional analysis of variance. Classification: Bayesian classifiers, linear and quadratic discriminant analysis, canonical discriminant analysis. Canonical analysis: Canonical correlation, principal components, factor analysis. Correlation models: Models for random phenomena which vary in time and space. Applications of SAS or R in the above areas.

02402/02403/02323, or another introductory course in statistics
knowledge of linear algebra

Lectures, tutorials, and computer exercises

The course is a general methodological course aimed at students interested in the analysis of multidimensional data or in achieving an overview over a number of the most common statistical methods.