John M. Noble
Mathematical Statistics
Institute of Applied Mathematics
University of Warsaw

October 2025 - January 2026

Multivariate Statistics

Course Information

Language: English
Type of course: elective

Place and Time

There are 14 lectures and 14 tutorials scheduled. These take place on Mondays. Lecture: 08.30 - 10.00 (room 5060) and tutorial 10.15 - 11.45 (room 2044: tutorial or computer lab). The dates are:
October 2025 6th, 13th, 20th, 27th
November 2025 3rd, 17th, 24th
December 2025 1st, 8th, 15th
January 2026 12th, 19th

Description

The course ‘Multivariate Statistics’ is a Master's level course, giving some statistical theory, with application in R.

The topics covered are:

• Nonparametric Density Estimation (histograms, kernel methods, projection pursuit)
• Multiple regression: model assessment and selection, shrinkage methods (eg LASSO)
• Linear Dimensionality Reduction: Principal Component Analysis, Canonical Correlation Analysis, Projection Pursuit
• Linear Discriminant Analysis.
• Recursive Partitioning and Tree-based Methods
• Artificial Neural Networks
• Support Vector Machines
• Clustering techniques: hierarchical and non-hierarchical partitioning methods, self organising maps (SOM), clustering variables, clustering based on mixture models (the EM algorithm as a tool for clustering and semi-supervised learning).
• Multidimensional Scaling and Distance Geometry
• Committee Machines, Bagging and boosting, random forests
• Latent Variable Models for Blind Source Separation
• Nonlinear Dimensionality Reduction and Manifold Learning
• Correspondence Analysis
• The multivariate Gaussian distribution, parameter estimation, the Wishart distribution.

Introduction to R

You should learn some R programming throughout the course. A reasonable introduction may be found here.

Assessment

Assessment is based on

• two data analysis assignments
• a take home written exam
• Tutorial participation.

Lecture and Tutorial Notes

These will be placed here throughout the course.

• 2024-10-06: 08.30 - 10.00 Lecture 1: Nonparametric Density Estimation
• 2024-10-02: 10.15 - 11.45 Tutorial 1: Nonparametric Density Estimation
• 2024-10-02: 10.15 - 11.45 Tutorial 1: R script

Data Files

Click here for the data directory.

(Last updated: 18th July 2025 by John M. Noble)