Applied Statistics

The notes are taken from the books required for the course:

G. James, D. Witten, T. Hastie, and R. Tibshirani. An Introduction to Statistical Learning: with Applications in R. Springer Texts in Statistics. Springer New York, 2013.
R.A. Johnson and D.W. Wichern. Applied Multivariate Statistical Analysis. Applied Multivariate Statistical Analysis. Pearson Prentice Hall, 2007.

📚 Course Syllabus

Exploring a multivariate dataset.
- Descriptive statistics and graphical displays.
- The geometry of a multivariate sample.
- Sample mean, covariance and correlation.
- Generalized variance and total variance.
- The metric induced by the covariance matrix.
Data representation and dimensional reduction.
- The analysis of the covariance structure, principal component analysis (PCA).
Discrimination, classification, clustering.
- Statistical classification: model, misclassification costs and prior probability.
- Bayesian supervised classification and the Fisher approach to discriminant analysis.
- Cross-validation for the evaluation of a classification function.
- Alternative approaches to classification: CART, support vector machines.
- Similarity measures.
- Unsupervised classification; hierarchical and nonhierarchical methods.
- DBSCAN.
- K-means and K-medoids.
- Multidimensional scaling.
Inference about mean vectors.
- The multivariate normal distribution, the Wishart distribution, the F distribution.
- Hotelling test.
  
  T2
- Confidence regions and simultaneous comparisons of component means.
- The Bonferroni method for multiple comparisons.
- Familywise Error Rate and False Discovery Rate.
- Comparisons of several multivariate means.
- ANOVA and MANOVA.
- Inference for Linear Models.
- Beyond Ordinary Least Squares: ridge regression, lasso, regularized least Squares.
- Random effects and mixed effects linear models.

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