Multivariate Statistics

elective courses

This course presents multivariate statistical theory and techniques. The topics covered are:

1) Asymptotic log likelihood ratio tests; Wald, Rao, Pearson; logistic regression.

2) Generalised Linear Models.

3) Model selection criteria (for example: AIC, BIC)

4) Shrinkage methods for linear regression (e.g. PCR, PSLR, Ridge and LASSO).

5) The multivariate Gaussian distribution, parameter estimation, the Wishart distribution.

6) Statistical tests for multivariate Gaussian data. (e.g. Hotelling)

7) The data matrix, geometrical representations and distances.

8) Principal Component Analysis and Canonical Correlation Analysis.

9) Non-parametric Density Estimation: histograms, kernel density estimation methods, optimal bin width, projection pursuit methods for multivariate densities.

10) Discriminant Function Analysis.

11) Clustering techniques, including logistic regression, self organising maps (SOM) and the EM algorithm as a tool for clustering and semi-supervised learning.

This course presents multivariate statistical theory and techniques. The topics covered are:

1) Asymptotic log likelihood ratio tests; Wald, Rao, Pearson; logistic regression.

2) Generalised Linear Models.

3) Model selection criteria (for example: AIC, BIC)

4) Shrinkage methods for linear regression (e.g. PCR, PSLR, Ridge and LASSO).

5) The multivariate Gaussian distribution, parameter estimation, the Wishart distribution.

6) Statistical tests for multivariate Gaussian data. (e.g. Hotelling)

7) The data matrix, geometrical representations and distances.

8) Principal Component Analysis and Canonical Correlation Analysis.

9) Non-parametric Density Estimation: histograms, kernel density estimation methods, optimal bin width, projection pursuit methods for multivariate densities.

10) Discriminant Function Analysis.

11) Clustering techniques, including logistic regression, self organising maps (SOM) and the EM algorithm as a tool for clustering and semi-supervised learning.

1. Izenman, A.J. Modern Multivariate Statistical Techniques, Springer 2008

2. T. J. Hastie, R. J. Tibshirani i J. Friedman, The Elements of Statistical Learning, Springer 2001.

3 The R Development Core Team, An Introduction to R, www.r-project.org.

4. E. Paradis, R for Beginners, www.r-project.org.

5. J.M. Noble Course notes on the course page

https://www.mimuw.edu.pl/~noble/courses/MultivariateStatistics/

1) Can build and evaluate linear and generalised linear statistical models, using modern techniques.

2) Understands the multivariate statistical theory that lies behind the techniques.

3) Can carry out canonical correlation analysis and principal component analysis.

4) Has a facility with classification techniques, discriminant function analysis, and other supervised learning techniques.

5) Has a facility with clustering techniques, including (for example) SOM (self organised maps)

6) Can implement all these techniques in R and has an understanding of the theoretical background.

Social competence

Understands the main methods of multivariate statistical data analysis and the theory behind these methods. Is able to perform a routine analysis in R.

Can analyse data and build simple models in collaboration with a naturalist, engineer or economist.

The assessment is in two parts:

1) Applications: assignments throughout the semester and a larger project at the end, requiring data analysis using R; assessment criteria will be a) correctness of the data analysis and b) clarity of the presentation of conclusions.

2) A take-home examination consisting of theoretical questions.

Both these components are given equal weight.