Online class, Tuesday May 11, 14h30-17h00

Multivariate Statistics [slides 1-44] Programme and bibliography. Introductory remarks regarding Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). A motivating example: the crayfish dataset. Some matrix concepts: orthogonal matrices; The classification of symmetric matrices through their quadratic forms; eigenvalues and eigenvectors and the spectral decomposition of symmetric matrices; properties and powers of diagonal matrices; powers of symetric matrices;the trace of a square matrix and the circularity of the trace; (co-)variance matrices as positive semi-definite matrices; variances and covariances of linear combinations of variables. PCA: a statistical introduction. The Rayleigh-Ritz Theorem. The definition of PCs and some properties. PCA in R. Exploring the PCs of the crayfish data.