20592 - STATISTICS AND PROBABILITY

The course aims at providing students with a solid theoretical background in statistics and probability. Building on a formal definition of probability, students are introduced to asymptotic results both in the independent sampling case and in the markovian case. Students are introduced to formal statistical reasoning both in the likelihood based approach and in the Bayesian approach to parametric inference . As well a brief introduction to nonparametric techniques is provided. Students are exposed to computational methods they can proficiently use to explore the conceptual challenges of inferential reasoning. The lectures switch between frontal lecturing, small group discussions and simulations. Students are introduced to the use of Python for coding the computational statistic techniques taught in the course.

• Asymptotics results in the i.i.d case.
• Markov Chains and ergodic theorems.
• Monte Carlo techniques.
• Maximum Likelihood approach to parametric inference.
• An introduction to nonparametric techniques.
• Bayesian approach to parametric inference.
• Markov Chain Monte Carlo tecniques.

• Define and explain rigorously the main notions of probability and statistical learning in the frequentist and bayesian approach.

• Write algorithms in Python for the implementation of computational statistic techniques, namely optimization and integration techniques.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Individual assignments
• Group assignments

As individual and group assignments students are asked to write codes in Python for the implementation of computational statistic techniques.

• Written exam: general exam is marked out of 31 and contributes 50% to the final mark.
• Periodic assignments: individual or group work. Marked out 31 contribute by 10% to the final mark.
• Project: Individual or group work. 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 work. Marked out 31 contributes by 40% to the final mark.

References to textbooks and papers and Python notebooks are provided.