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 13 lectures and 13 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). Thursday 13th November 2025 is an ‘honourary Monday’, so the dates are:
October 2025 6th, 13th, 20th, 27th
November 2025 3rd, 13th 17th, 24th
December 2025 1st, 8th, 15th
January 2026 12th, 19th
OBS: These are Mondays, except for Thursday 13th November

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.

• 2025-10-06: 08.30 - 10.00 Lecture 1: Nonparametric Density Estimation
• 2025-10-06: 10.15 - 11.45 Tutorial 1: Nonparametric Density Estimation
• 2025-10-06: 10.15 - 11.45 Tutorial 1: R script
• 2025-10-13: 08.30 - 10.00 Lecture 2: Generalised Linear Models I
• 2025-10-13: 10.15 - 11.45 Tutorial 2: Generalised Linear Models I
• 2025-10-13: 10.15 - 11.45 Tutorial 2: R script
• 2025-10-20: 08.30 - 10.00 Lecture 3: Generalised Linear Models II
• 2025-10-20: 10.15 - 11.45 Tutorial 3: Generalised Linear Models II
• 2025-10-20: 10.15 - 11.45 Tutorial 3: R script
• 2025-10-27: 08.30 - 10.00 Lecture 4: Model Selection Criteria
• 2025-10-27: 10.15 - 11.45 Tutorial 4: Generalised Linear Models III
• 2025-10-27: 10.15 - 11.45 Tutorial 4: R script
• 2025-11-03: 08.30 - 10.00 Lecture 5: Biased Regression Methods
• 2025-11-03: 10.15 - 11.45 Tutorial 5: Biased Regression Methods
• 2025-11-03: 10.15 - 11.45 Tutorial 5: R script
• 2025-11-13: 08.30 - 10.00 OBS This is Thursday Lecture 6: Penalised Regression Methods
• 2025-11-13: 10.15 - 11.45 Tutorial 6: Penalised Regression Methods
• 2025-11-13: 10.15 - 11.45 Tutorial 6: R script
• Assignment 1. Deadline: 13:00 Monday 1st December 2025
• 2025-11-17: 08.30 - 10.00 Lecture 7: Discriminant Function Analysis
• 2025-11-17: 10.15 - 11.45 Tutorial 7: Discriminant Function Analysis
• 2025-11-17: 10.15 - 11.45 Tutorial 7: R script
• 2025-11-25: 08.30 - 10.00 Lecture 8: CART: Classification and Regression Trees
• 2025-11-25: 10.15 - 11.45 Tutorial 8: CART: Classification and Regression Trees
• 2025-11-25: 10.15 - 11.45 Tutorial 8: R script
• 2025-12-01: 08.30 - 10.00 Lecture 9: Bagging, Boosting and Random Forests
• 2025-12-01: 10.15 - 11.45 Tutorial 9: Bagging, Boosting and Random Forests
• 2025-12-01: 10.15 - 11.45 Tutorial 9: R script
• 2025-12-08: 08.30 - 10.00 Lecture 10: Canonical Correlation Analysis
• 2025-12-08: 10.15 - 11.45 Tutorial 10: Canonical Correlation Analysis
• 2025-12-01: 10.15 - 11.45 Tutorial 10: R script

Data Files

Click here for the data directory.

(Last updated: 1st December 2025 by John M. Noble)