Insegnamento a.a. 2024-2025

• Thinking like a Bayesian: subjective probability.
• Statistical inference as the update of belief: Bayes' Theorem.
• Predictive approach to statistical inference: exchangeability and de Finetti's representation theorem.
• Selection of prior distributions: conjugate families.
• Parametric inference: point estimation, interval estimation, hypothesis testing, model selection.
• Stochastic simulation methods: Monte Carlo, Gibbs sampler, and Metropolis-Hastings.
• Posterior prediction and validation.
• Bayesian hierarchical models and partial exchangeability.
• Bayesian regression and classification: linear regression, regularization, bias-variance tradeoff, Gaussian processes, and naïve Bayes.
• Bayesian clustering: mixture models and random partitions.

• Illustrate the concept of subjective probability and its role in Bayesian inference.
• Comprehend the logical foundations of Bayesian data analysis.
• Explain the theoretical basis of Bayesian parameter estimation, hypothesis testing, interval estimation, and model selection.
• Identify appropriate prior distributions and the most effective computational techniques based on the statistical problem.

• Select suitable Bayesian statistical models for a given problem.
• Compute posterior distributions using analytical methods and computational techniques.
• Interpret and communicate the results obtained from Bayesian analysis.
• Apply Bayesian statistical methods to real-world problems.
• Critically evaluate the strengths and limitations of Bayesian approaches in different contexts.

• Lectures
• Practical Exercises
• Collaborative Works / Assignments

The teaching and learning activities are based on lectures that present Bayesian statistics with a main attention to methodology, theory, and computational methods. Furthermore, these aspects are illustrated through R code "scripts" explained during lectures and available on the Bboard platform, which students can upload to their own computers and use/modify directly to better understand the actual role of various models and proposed initial distributions. The group work, which contributes to the final evaluation, allows students to delve into a topic of their interest (theoretical or applied).

Student evaluations is based on:

• One between group or individual assignment, to verify the student's ability to use and understand the methodologies and techniques presented in class in situations other than those explicitly considered in the course. [optional]
• Written exam (either a single general or midterm and end of semester exams), consisting of exercises, multiple-choice, and theory questions, which aim to evaluate both the understanding of the proposed methodologies and the student's ability to apply the analytical tools illustrated during the course.

Grading rule: Let X denote the grade of the written individual exam and let Y be the grade of the group assignment. Then, if Y is greater than or equal to X, the final grade is 0.3*Y+0.7*X. Otherwise, if Y is less than X, the final grade is X.

Lecture notes are provided via BBoard.

The course relies, mostly, on the books:

• A. A. JOHNSON, et al., Bayes Rules! An introduction to applied Bayesian modeling. 2022 by Chapman & Hall.
• P.D. HOFF, A first course in Bayesian statistical Methods, New York, Springer-Verlag, 2009.   
• A. GELMAN, et al., Bayesian Data Analysis, Third Edition, CRC Press, 2013.

Students who are interested in deepening, individually, specific concepts are provided with additional reading materials upon request. These additional materials are not object of final evaluation.