- To provide a solid understanding of the theoretical and practical foundations of Bayesian inference in the context of machine learning. - To introduce students to the design, construction and analysis of Bayesian networks. - To train in the use of advanced computational methods-including Hamiltonian Monte Carlo (HMC), INLA, Variational Bayes (VB) for solving real-world problems. - Develop skills in data analysis through the techniques taught in the course - Introduce and apply Bayesian spatial analysis in multidisciplinary contexts. - Integrate theory with practice through theoretical/practical activities in the use of RStudio and associated tools (R, RStan and eventually TensorFlow), encouraging critical debate and discussion of practical cases.

1. Introduction to Bayesian Networks 2. Construction and analysis of simple Bayesian networks in R. 3. Advanced Bayesian Networks 4. Advanced Computational Methods: Hamiltonian Monte Carlo (HMC) and Introduction to INLA; Variational Bayes (VB) and Parallel MCMC. 5. Cluster Analysis with Mixture Models 6. Dynamic Linear Models (DLMs) 7. Bayesian Spatial Analysis

The sessions will be developed in a theoretical/practical format through the use of the computer, using the RStudio environment (https://www.rstudio.com) and R language (https://www.r-project.org). The teacher will indicate the packages to be used, based on RStan (https://mc-stan.org/users/interfaces/rstan) and, where appropriate, on TensorFlow (https://www.tensorflow.org). After explaining the content of Bayesian inference applied to a specific real problem, the possible solution of the case will be illustrated by means of a practical demonstration in R, emphasising the critical elements of the solution and promoting discussion of the results obtained with the students.