(2023/2024) 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.

You can view/download the PDF here. In the notes folder, you can also see the source code.

For any issue, use the appropriate section.

Course Syllabus

According to the official course syllabus:

1. 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.
2. Data representation and dimensional reduction.
   • The analysis of the covariance structure, principal component analysis (PCA).
3. 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.
4. Inference about mean vectors.
   • The multivariate normal distribution, the Wishart distribution, the F distribution.
   • Hotelling $T^2$ test.
   • 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.