Statistical data analysis

Semestr: Winter

Range: 2P+2C

Completion:

Credits: 6

Programme type:

Study form: Fulltime

Course language: English

Time table at FEE

Summary:

This course builds on the skills developed in introductory statistics courses. It is practically oriented and gives an introduction to applied statistics. It mainly aims at multivariate statistical analysis and modelling, i.e., the methods that help to understand, interpret, visualize and model potentially high-dimensional data. It can be seen as a purely statistical counterpart to machine learning and data mining courses.

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Course syllabus:

1. Introduction, motivation, a course map, review of the basic statistical terms and methods.
2. Dimension reduction (PCA and kernel PCA).
3. Dimension reduction (other non-linear methods).
4. Clustering (basic methods, spectral clustering).
5. Clustering (biclustering, semi-supervised clustering)
6. Multivariate confirmation analysis (ANOVA and MANOVA).
7. Discriminant analysis (categorical dependent variable, LDA, logistic regression).
8. Multivariate regression (continuous dependent variable, linear regression, p-values, overfitting)
9. Multivariate regression (non-linear models, polynomial and local regression).
10. Anomaly detection.
11. Robust statistics.
12. Empirical studies, their design and evaluation.
13. Power analysis.
14. The final review, spare lecture.

Seminar syllabus:

1. Statistical testing, t-test, significance, power of the test.
2. Simple linear regression.
3. Shrinked linear regression
4. Non-linear regression
5. Discriminant analysis.
6. Generalized linear models
7. Mid-term test, the final assignment
8. Dimension reduction.
9. Robust statistics
10. Anomaly detection
11. Empirical study design, power analysis.
12. Clustering
13. Time series analysis.
14. The final assignment – team presentations.

Literature:

1. Hair, J. F., et al.: Multivariate Data Analysis: A Global Perspective. 7th ed., Prentice Hall, 2009.
2. James, G. et al.: An Introduction to Statistical Learning with Applications in R., Springer, 2013.

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