Statistical data analysis 1000-714SAD

1. Basic notions of probability calculus and statistics: random variables, their distributions, expected value and variance, probability space.
2. Basic notions of statistics: statistical space, random experiment, statistic, statistical model, model evaluation methods.
3. Parameter estimation. Bias and efficiency, maximum likelihood estimatoes, confidence intervals.
4. Summary and visualisation of data. Quantile-quantile plots. Histograms, kernel density estimation, boxplot.
5. Hypothesis testing. The notion of a statistical hypothesis, the procedure of hypothesis testing, type I and type II errors, power of a test, Neyman-Pearson lemma, parametric statistical significance tests, significance tests for a mean, significance tests for a variance.
6. The notion of p-value and potential misunderstandings and misusage, effect size, multiple hypothesis testing.
7. Useful statistical tests. Statistical significance test for two means, non-parametric tests for two medians, Pearson's chi-squared test, analysis of variance.
8. Linear regression, simple, multiple, with extensions: assumptions, parameter estimation, evaluation of goodness of fit.
9. Classification. Logistic regression, LDA, QDA, KNN.
10. Resampling methods. Cross-validation, bootstrap.
11. Model selection and regularisation. Feature selection, usage of a validation set, usage of cross-validation, analysis of high-dimensional data, lasso and ridge regression, partial least squares.
12. Tree-based models: decision trees, bagging, random forests, boosting
13. Support vector machines. Separating hyperplanes, maximum margin classifyier, support vector machines.
14. Dimensionality reduction. PCA.
15. Unsupervised learning. The notion of clustering, methods of hierarchical clustering and k-means.
16. Nonlinear models. Polynomial regression, splines, generalized additive models.