20592 - STATISTICS AND PROBABILITY

The course aims at providing students with a solid background in statistics and probability needed for running basic and advanced data analyses. Building on knowledge of probability and calculus, students are introduced to formal statistical reasoning with an emphasis of understanding the logic behind data analysis procedures. Students are exposed as well to advanced methods for data description and to computational tools they can proficiently use to analyze data and explore the conceptual challenges of inferential reasoning. Statistical models for classification and prediction is discussed in the last part of the course. The lectures switch between frontal lecturing, small group discussions and simulations. Students are introduced to the use of Python for retrieving and describing data, writing codes for implementing statistical methods and running model based data analyses.

• Advanced methods for data description and visualization.
• Dimension reduction and clustering.
• Probability: notable distributions, limit theorems.
• Statistical inference and prediction: Maximum Likelihood approach.
• Algorithms for optimization and integration.
• Generalized Linear Models.
• Classification models.

• Define and explain rigorously the main notions of probability and statistical learning.

• Design, apply and implement proper statistical analsys and uncertainty quantification.
• Prepare effective reports.

• Face-to-face lectures
• Case studies /Incidents (traditional, online)
• Group assignments

Group assignments: statistical analysis of real data.

• Written exam: general exam is marked out of 31 and contributes 50% to the final mark.
• Periodic assignments: individual or group work aiming at building the skills needed for the final project. Marked out 31 contribute by 10% to the final mark.
• Project: Individual or group real data analysis. Marked out 31 contributes by 40% to the final mark.

• Written exam: general exam is marked out of 31 and contributes 60% to the final mark.
• Project: Individual or group real data analysis. Marked out 31 contributes by 40% to the final mark.

References to textbooks and papers and Python notebooks are provided.