Statistical decision theory: risk, decision rules, loss and utility functions, Bayesian expected loss, Frequentist risk.

Bayesian Analysis: Bayes theorem, prior, posterior and predictive distributions, conjugate models (Normal-Normal, Poisson-Gamma, Beta-Binomial), Bayesian point estimation, credible intervals and hypothesis testing, Bayes factors and model selection. Comparison with Frequentist approaches.

Implementation: Asymptotic approximations (Laplace approximation, Variational Bayes, Monte Carlo methods, stochastic simulation), Markov Chain Monte Carlo (MCMC) simulation (Gibbs sampler, Metropolis-Hastings algorithm). Computer tools (R, WinBUGS).

**Applications:** Linear models in Regression and Classification (Bayesian Linear Regression, Generalized Linear Models, Logistic Regression), Cluster Analysis and Mixture Modeling, Hierarchical/ Multilevel Models.