John M. Noble

Mathematical Statistics

Institute of Applied Mathematics

University of Warsaw

October 2021 - January 2022

## Multivariate Statistics

## Course Information

**Language:** English

**Type of course:** elective

## Description

The course ‘Multivariate Statistics’ is a Master's level course, which builds on the foundations laid in the course *Statistics * and draws heavily on the concepts from that course.

The topics covered are:## Introduction to R

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

## Assessment

Assessment is based on

To pass the course, it is necessary to pass the written examination on multivariate statistical theory and also to submit satisfactory computer assignments.## Lecture Notes, Tutorial Exercises and Solutions, Examination

Click here for a pdf of the lecture notes, tutorial exercises and solution and the examinations (theoretical and practical).
## Data Files

Click here for the data directory.

*(Last updated: 10th February 2022 by John M. Noble)*

Mathematical Statistics

Institute of Applied Mathematics

University of Warsaw

October 2021 - January 2022

The topics covered are:

- Asymptotic log likelihood ratio tests; Wald, Rao, Pearson; logistic regression.
- Generalised Linear Models.
- Model selection criteria (for example: AIC, BIC)
- Shrinkage methods for linear regression.
- The multivariate Gaussian distribution, parameter estimation, the Wishart distribution.
- Statistical tests for multivariate Gaussian data.
- The data matrix, geometrical representations and distances.
- Principal Component Analysis
- Canonical Correlation Analysis.
- Non-parametric Density Estimation: histograms, kernel density estimation methods, optimal bin width, projection pursuit methods for multivariate densities.
- Discriminant Function Analysis.
- Clustering techniques, including logistic regression, self organising maps (SOM) and the EM algorithm as a tool for clustering and semi-supervised learning.

- A written examination (60 %)
- Two data analysis assignments (40 %)

To pass the course, it is necessary to pass the written examination on multivariate statistical theory and also to submit satisfactory computer assignments.