Advanced bayesian inference

Carlo Trivisano

  • Date:

    01 JANUARY
    -
    30 MAY 2026
     from 11:00 to 13:00

  • Event location: Aula IV, Department of Statistical Sciences, Via Belle Arti 41 (STAT PhD Classes Virtual Room on need)

  • Type: Cycle 40 - Elective Courses

Aim: To provide a solid knowledge about the theoretical foundations of Bayesian statistics, including concepts such as subjective probability, Bayesian inference, belief updating, and prior and posterior distributions. Advanced computational methods will be treated in detail, in particular for the estimation of Generalised Linear Mixed Models. 

Learning outcomes: At the end of the course Students will build the necessary skills to apply Bayesian statistics in diverse fields of interdisciplinary research and to estimate Bayesian models by means of Markov Chain Monte Carlo (MCMC) methods, with a particular focus on Hamiltonian Monte Carlo and Integrated Nested Laplace Approximation (INLA) as implemented in the R packages Stan and INLA.

 Course contents

  • Subjective Probability, Bayes theorem and belief updating
  • Representation theorem (de Finetti)
  • Conjugate and non-conjugate models
  • Bayesian hypothesis testing
  • Bayesian linear and generalized linear models
  • Bayesian mixed models
  • Computational methods: Markov Chain Monte Carlo (MCMC), Hamiltonian Monte Carlo and Integrated Nested Laplace Approximation.

Highlights