#### LM in Scienze Statistiche e Decisionali

##### BAYESIAN MODELLING

This is an introductory course about Bayesian inference and Bayesian modelling for data analysis. We will balance between theoretical and analytical tools and practice. In particular for practical implementation of Bayesian models on real data we will make use of some software for Bayesian modelling and inference (R, BUGS/JAGS, INLA).

The course will cover:

**Introduction to Bayesian Thinking***In this part we will cover basic definitions, Bayesian model, Bayesâ€™ theorem. Subjective prior elicitation and some noninformative or default prior choices (e.g. Jeffreysâ€™Rule). Conjugate analysis. Techniques and tools for characterizing and summarizing posterior distributions.**Bayes Factor*, introduction to multi-model inference and Bayesian model choice.**Multiparameter Inference***In this part we will cover multivariate normal and multinomial models and introduces to approximate random sampling from a multivariate distribution. Bayesian inference in the presence of missing data.***Hierarchical Models, Model Checking and Linear Models***In this last part we will cover*the Bayesian approach for hierarchical modelling and linear regression. Linear and generalized linear mixed effects models. It also considers posterior predictive checking, sensitivity analysis, and goodness-of-fit statistics.**MC & MCMC***Introduction to Monte Carlo and Monte Carlo Markov Chain sampling techniques for approximating expectations and distributions: Gibbs Sampling and Metropolis Hastings algorithms.*

- Teacher: Dimitris Fouskakis
- Teacher: Luca Tardella