Multivariate Data Analysis

The course provides the basic theory and methods for multivariate data analysis and lays a solid foundation for learning more advanced methods and algorithms in the next step. It starts from multivariate Gaussian distribution (MGD) and its generalization, the Gaussian mixture model. The maximum likelihood estimation (MLE) and the EM algorithm are discussed. Based on MGD, statistical inference approaches (Hotelling's T square test, multivariate analysis of variance, MANOVA), classification methods (Linear discriminant analysis and logistic regression), and clustering analysis methods are covered. Furthermore, based on the projection ideas, different eigen-decomposition based methods for dimensionality reduction, such as principal component analysis (PCA), factor analysis (FA), canonical correlation analysis (CCA), and partial least squares (PLS) are introduced. Models for regression analysis with colinear explanatory variables such as principal component regression (PCR) and PLS regression are also included. Module 1 (5 hp): *Theory and applications* The module covers multivariate distributions with special emphasis on the multivariate normal distribution and its properties. The EM algorithm for finding maximum likelihood estimation of GMM is introduced. Further, methods for inference concerning mean vectors, and variance and correlation matrices are treated, along with methods for projections, classification, and clustering analysis.   Module 2 (2,5 hp): *Computer labs* Multivariate data analysis with suitable statistical software. The module includes written and oral presentation of results.