Prof. Bernardo Nipoti, Università degli Studi di Milano-Bicocca
Chair: Prof. Enrico Ripamonti, Università degli Studi di Brescia
When: May 26th, 2026, 10:00 AM - 4.00 PM
Where: Sala della Biblioteca, via San Faustino 74/b
Bayesian nonparametric inference has become an increasingly important paradigm in modern statistics, providing a flexible and principled framework for probabilistic modeling and data analysis. By placing prior distributions on infinite-dimensional objects, Bayesian nonparametric methods allow for accurate estimation of complex functions such as probability distributions, regression functions, and hazard rates. Rooted in de Finetti’s foundational work on exchangeability, the field has evolved through key methodological developments, most notably the introduction of the Dirichlet process, and has undergone substantial growth over the last two decades, driven by advances in computational algorithms and their successful application to a wide range of challenging problems.
This short course provides an introduction to Bayesian Nonparametric Statistics at the PhD level. It begins with a concise review of the Bayesian paradigm, with emphasis on probabilistic modeling, prior specification, posterior inference, and computation. The assumption of exchangeability is then introduced as a key modeling principle in Bayesian inference, providing a rationale for the use of prior distributions. The Dirichlet process is presented as the most prominent Bayesian nonparametric prior, along with its main theoretical properties and constructive representations. Building on this framework, the course focuses on Dirichlet process mixture models as flexible tools for density estimation and clustering. Extensions beyond the Dirichlet process are subsequently discussed, with particular attention to the Pitman–Yor process and its implications for modeling power-law behavior and richer clustering structures. Computational aspects of Bayesian nonparametrics are addressed throughout the course, including Markov chain Monte Carlo methods as well as marginal and conditional sampling schemes. The theoretical concepts are complemented by concrete examples and hands-on implementations in R, with specific use of the BNPmix package for fitting and exploring Bayesian nonparametric mixture models.