We will be using the RStan interface to Stan, which can be installed by following the instructions at https://github.com/stan-dev/rstan/wiki/RStanGetting-Started 

DAY 1: Foundations of Bayesian inference in theory and practice 

• What is Bayesian inference? 

• Generative models, prior, likelihood, posterior 

• Advantages and disadvantages of Bayesian methods (comparisons with other approaches to inference) 

• Bayesian data analysis workflow 

• Introduction to computation with Markov Chain Monte Carlo (MCMC) 

• Challenges of implementing MCMC in practice (i.e., why do we need Stan?) 

• Introduction to Stan with simple examples 

DAY 2: Bayesian applied regression models 

• Bayesian perspective on linear and generalized linear models (GLMs) 

• How to think about priors for GLMs 

• Programming and fitting GLMs in Stan (using RStan, the R interface to Stan) 

• Approaches to inference/prediction using GLMs 

• Communicating results from regression models 

DAY 3: Model checking, model comparison, and model selection/averaging 

• Graphical and numerical model checking (posterior predictive checks) 

• Comparing models based on different criteria 

• Prediction vs explanation 

• Model selection vs model averaging 

DAY 4-5: Hierarchical/Multilevel modeling 

• Theory of Bayesian hierarchical modeling, partial pooling 

• Programming and fitting hierarchical models in Stan 

• Understanding and diagnosing MCMC problems when fitting hierarchical models 

• Using reparameterizations to solve computational problems when fitting hierarchical models 

• If we have time we can cover more advanced topics like covariance with temporal and/or spatial structure 

Professors:

Leonardo Egidi (University of Trieste) & Gaia Di Credico (University of Trieste) 

Leonardo Egidi is a postdoctoral researcher at the Department of Business, Economics, Mathematics and Statistics (DEAMS) of the University of Trieste, professor of the course Bayesian Statistics, and teaching assistant of the course Statistical Methods for Data Science in the same university. He received his PhD in Statistics at the Department of Statistical Sciences of the University of Padova. His research mainly focuses on both theoretical and applied Bayesian statistics, with a particular attention to mixture models, robust priors, relabelling algorithms and hierarchical models for sports data, such as football and volleyball. He is an R packages developer and he also provides statistical consultancy to small firms, hospitals and medical departments. He has been elected in the board of the young section of the Italian Statistical Society (ySIS). 

Gioia Di Credico is a postdoctoral researcher at the Department of Business, Economics, Mathematics and Statistics (DEAMS) of the University of Trieste, and teaching assistant of the course Bayesian Statistics in the same university. She received her PhD in Statistics at the Department of Statistical Science of the University of Padova. Her work mainly concentrates on the development and application of Bayesian statistical methods in epidemiology. It focuses on generalised linear models with splines, variable selection techniques and Bayesian hierarchical models.