Course 2025-2026 a.y.

• Thinking like a Bayesian: subjective probability, Bayes' Theorem, and belief updates.
• Predictive approach to statistical inference: exchangeability and de Finetti's representation theorem.
• Parametric inference: conjugate priors, point estimation, interval estimation, hypothesis testing, model selection, posterior prediction, and validation.
• Stochastic simulation methods: Monte Carlo, ABC, Gibbs sampler, and Metropolis-Hastings.
• Bayesian hierarchical models: partial exchangeability, borrowing of information, and group comparison.
• Bayesian regression and classification: linear regression, regularization, bias-variance tradeoff, Gaussian processes, and naïve Bayes.
• Bayesian clustering: mixture models and random partitions.
• Bayesian generative network models.

• 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, model selection, and prediction.
• Identify appropriate prior distributions, generative models, 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

The teaching and learning activities are based on lectures that present Bayesian statistics with a main focus on 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 computers and use/modify directly to better understand the actual role of various models and proposed initial distributions.

Student evaluation is based on a final written exam 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.

Lecture notes and exercises are provided via BBoard.

The course partially relies 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.