John M. Noble
Mathematical Statistics
Institute of Applied Mathematics
University of Warsaw
October 2022 - January 2023
Multivariate Statistics
Course Information
Language: English
Type of course: elective
Place and Time
There will be 14 lectures and 14 tutorials. These take place on Mondays, with one additional Wednesday (2nd November). Lecture: 08.30 - 10.00 (room 5060) and tutorial 10.15 - 11.45 (room 2044: computer lab). The dates are:
October 2022 10th, 17th, 24th
November 2022 2nd, 7th, 14th, 21st, 28th
December 2022 5th, 12th 19th
January 2023 9th, 16th 23rd
Description
The course ‘Multivariate Statistics’ is a Master's level course, giving some statistical theory, with application in R.
The topics covered are:
- 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.
- 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.
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
Tutorial participation will also be taken into account.
Lecture and Tutorial Notes
Data Files
Click
here for the data directory.
(Last updated: 7th December 2022 by John M. Noble)