Laurea Magistrale (M.Sc.) in Stochastics and Data Science

Bayesian statistics

Bayesian statistics

Academic year 2018/2019

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

Bayesian statistics constitutes the main alternative approach to classical statistical inference, which is based on frequentist principles. Its approach and advantages have nowadays found widespread appreciation by the most diverse scientific communities, as witnesses by the countless registered applications of Bayesian methods to virtually any applied discipline. The course aims at providing a modern overview of Bayesian statistical methods, covering the fundamentals of both the parametric and the nonparametric approach. The course will focus on the key probabilistic and foundational concepts, stochastic modelling tools and most widely used computational strategies at the basis of the most recent advances in the field.

A short module of the course, included in the overall courseload, will be taught by Visiting Professor Omiros Papaspiliopoulos (Universitat Pompeu Fabra) on Scalable algorithms in modern Bayesian computation (see International visiting professors).

Results of learning outcomes

Course delivery

The course consists of roughly 80% of class lectures, and 20% of computer lab sessions.

Learning assessment methods

The exam consists in the oral verification of the material covered in class on the parametric and the nonparametric module. The final mark will be the average of the two evaluations given by the two lecturers on the respective modules (parametric and nonparametric).
In addition to the above, students can optionally present and discuss a scientific paper (e.g., one of those referenced during the course) with the aid of a slide presentation (in which case they should bring their own personal device to the exam). The students are encouraged to agree upon the paper to be presented with the teacher whose module is more relevant for the topic. In this case, the examination on such module will be shorter. Only one paper to one teacher can be presented.

Program

Bayesian parametric statistics:

- Motivation and foundations of Bayesian inference: exchangeability and de Finetti's representation theorems
- Conjugacy, posteriors and parametric families of conjugate models
- Markov chain Monte Carlo methods for parametric inference

Bayesian nonparametric statistics:

- The Bayesian nonparametric framework
- The Dirichlet process: definition and properties
- Constructions of the Dirichlet process
- Hierarchical priors derived from the Dirichlet process
- Prior models beyond the Dirichlet process

Lecture notes will be made available. Additional suggested reading are:

HOFF, P.D. (2009). A First Course in Bayesian Statistical Methods. Springer.
GHOSAL, S. and VAN DER VAART, A. (2017). Theory of nonparametric Bayesian inference. Cambridge University Press.
HJORT, N., HOLMES, C., MUELLER, P. and WALKER, S.G. (eds.) (2010). Bayesian Nonparametrics. Cambridge University Press.
GHOSH, J.K. and RAMAMOORTHI, R.V. (2003). Bayesian Nonparametrics. Springer.

Class schedule

Note

This course will be delivered at the ESOMAS Department.

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums