Single-Course Engelsk 5 ECTS

# Multivariate Statistics

## Overall Course Objectives

To give the participants a more thorough understanding of statistical methods with special emphasis on revealing the structure of multidimensional data. The participants are expected to learn to assess multidimensional (linear and non-linear) relations and estimate best predictors, to analyze the influence of complicated experimental designs on (uni- or multi-dimensional) measurements, to assess whether multidimensional data can be reduced to lower dimensionality and in doing this, to assess whether a number of features in a population can be described with a few “factors”, to discriminate between different populations using simple (linear) functions of measurements of different features of the single individuals, to assess the structure of and relations between phenomena which vary in time. Lastly to be able to use a standard statistical computer program (SAS or R) and be able to interpret the output and relate it to the course curriculum.

See course description in Danish

Learning Objectives

• 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

Course Content

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.

Recommended prerequisites

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

Teaching Method

Lectures, tutorials, and computer exercises

Faculty

Remarks

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.

See course in the course database.

## Registration

Language Engelsk 13 weeks Compute DTU Lyngby Campus 02409 Candidate Week 36 Week 49 Mon 8-12
Price 9.250,00 DKK