This is a set of lectures within Bayesian Statistics class of the Mathematics for daTa scieNce study plan

# Antonio Canale

Personal website
Bio Antonio Canale graduated in Statistics and Computer Science at the University of Padova in 2008 and got a PhD in Statistics in the same University in 2012. During the PhD he visited Duke University where he focused on Bayesian Nonparametrics models and methods. After the PhD he became Assistant professor at the University of Turin and research affiliate of the Statistics Initiative of Collegio Carlo Alberto. In 2017 he moved back to Padova where he is now Associate professor of Statistics where he teaches both introductory and advanced statistical courses. His research interests touch both the theoretical, methodological, and computational aspects of Statistics; the statistical methods that he developed have applications across many disciplines, ranging from economics and social-sciences to biosciences.

## Prerequisites

• Parametric Bayesian inference
• Convergence of random variables
• Markov Chain Monte Carlo methods for posterior approximation (Metropoli-Hasings, Gibbs sampling)
• Basic knowledge of the R software

## Course Description

Statistical inference involves first setting up a model for data in terms of certain unknown parameters. Bayesian analysis tackles this problem by placing a prior distribution on these parameters and then deriving and using relevant aspects of the induced posterior distribution. Bayesian nonparametrics is the extended branch of such modelling and analyses where the parameter of the model is lies on an infinite dimensional space, as when one models an unknown density, regression, or link function. This calls for more complex mathematics and computational schemes than for the classical cases where the parameter is of finite dimension.

## List of topics

• Finite mixture models
• The Dirichlet process
• The Pitman-Yor process
• Nonparametric mixture models
• Bayesian posterior consistency
• Computational aspects of nonparamtric mixtures
• Case studies and R implementations
• The R package BNPmix

## References & study material

1. Hjort, N. L., Holmes, C., MÃ¼ller, P., & Walker, S. G. (Eds.). (2010). Bayesian nonparametrics Cambridge University Press
2. Canale, A., Lijoi, A., Pruenster I., (2016), Bayesian Nonparametrics. In Wiley StatsRef: Statistics Reference Online, John Wiley & Sons, Ltd.
3. Corradin, R., Canale, A., & Nipoti, B. (2021). BNPmix: An R Package for Bayesian Nonparametric Modeling via Pitman-Yor Mixtures. Journal of Statistical Software, 100, 1-33

## Schedule

• 2022/04/26 9.30-12.30, Room A105 @ Povo 1
• 2022/05/26 8.30-11.30, Room A219 @ Povo 1

## Details

• Venue: Polo Scientifico e Tecnologico F. Ferrari
• Language: English
• The participation is free. Please send an email to Prof. Claudio Agostinelli. This is important to book the approrpiate room.