Statistical Data Analysis
Semestr: Winter
Range: 2P+2C
Completion:
Credits: 6
Programme type:
Study form: Fulltime
Course language: Czech
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.
Keywords:
multivariate data analysis multivariate regression clustering dimensionality reduction anomaly detection power analysis
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. Programming in R, introduction.
2. R libraries, statistical packages, learning package Swirl.
3. Data visualization in R.
4. Dimension reduction - assignment.
5. Clustering - assignment.
6. Multivariate confirmation analysis - assignment.
7. Discriminant analysis - assignment.
8. Mid-term test.
9. Multivariate linear regression - assignment.
10. Multivariate non-linear regression - assignment.
11. Anomaly detection - assignment.
12. Empirical study design - assignment.
13. Power analysis - assignment.
14. Spare lab, credits.
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.