Course Syllabus
Aims
The aim of the course is to introduce multivariate statistical modeling and supervised/unsupervised statistical learning, making students able to identify the most suitable techniques for describing and predicting a phenomenon, in relation to the type of data available.
Students are invited to consult the syllabus of the entire course for details regarding learning- and skill-related objectives.
Contents
• Brief recall of the basic notion of statistical inference (point and interval estimation, hypothesis tests).
• Linear regression.
• Logistic regression.
• Principal component analysis.
• Linear discriminant analysis.
• K-means clustering.
• Hierarchical clustering.
• Use of the R software environment on data related to sustainability.
Detailed program
• Review of basic probability theory and statistical inference to recall the notion of confidence interval and hypothesis test.
• Simple linear regression: estimating the coefficients and assessing the accuracy of the coefficient estimates.
• Multiple linear regression: estimating the coefficients and assessing the accuracy of the coefficient estimates, linear model selection, prediction.
• Logistic regression: estimating the coefficients and assessing the accuracy of the coefficient estimates, variable selection, prediction.
• Cross-validation to evaluate the performance of a statistical model.
• Dimensionality reduction with the principal components analysis: estimation of principal components and their interpretation, biplot.
• Linear discriminant analysis: estimating discriminant functions, cluster prediction based on linear discriminant scores.
• K-means clustering and hierarchical clustering.
Prerequisites
• Basis of probability theory and knowledge of the most relevant continuous and discrete random variables.
• Basic notions of statistical inference: point estimation, confidence interval hypothesis testing.
• Linear algebra.
• matrix theory.
• Optimization of functions of several variables.
Teaching form
3 CFUs of mixed theoretical and interactive lessons in the classroom (24 hours):
• 8 two-hour lectures, in person, Delivered Didactics;
• 4 two-hour lectures, in person, discussing problems/exercises, Mixed Didactics.
Attendance to lectures and interactive exercises is highly recommended.
Textbook and teaching resource
• James G., Witten D., Hastie T. and Tibshirani R. (2021). An Introduction to Statistical Learning, with applications in R (2nd edition). Springer Verlag.
• Hastie T. , Tibshirani R., Friedman J. (2021). The Elements of Statistical Learning (2nd edition). Springer Verlag.
• Material provided by the lecturer.
Semester
I Semester (December - January)
Assessment method
The exam at the end of the module consists in a written test with open-ended questions to assess the student's knowledge, jointly with the development of an application in R on real data.
An oral discussion can be requested by the lecturer.
The final score will be between 18/30 and 30/30 cum laude, based on the overall assessment considering the following criteria:
(1) knowledge and understanding;
(2) ability to connect different concepts;
(3) autonomy of analysis and judgment;
(4) ability to correctly use scientific language.
Office hours
Always, after scheduling an appointment via e-mail.
