Personal repository for the Bayesian Statistics course of Data Science and Scientific Computing MSc @ UniTS and SISSA by Prof.Francesco Pauli and Prof. Leonardo Egidi.
CFU: 6.
Aims: understand the Bayesian inferential paradigm and its difference with respect to classical inferential paradigm. Being able to specify and estimate a range of models within the Bayesian approaches, assess the quality of the models and interpret the results.
Content:Introduction to Bayesian inference (with refresh of probability calculus and likelihood inference), Single parameter models: binomial, normal, Poisson Bayesian estimate, credibility interval (HPD), Predictive distribution (PPP), exchangeability Non informative/ weak informative / reference prior, Multiparameter models: multivariate normal, known and unknown, variance Asymptotic approximation (parallel with classical inference), Hierarchical models, Regression model MCMC general introduction (Gibbs-Metropolis), Programming an MCMC algorithm in R, Introduction to Stan and use of Stan for estimation, (optional) sketch of other approximation methods (Laplace, INLA); model selection and averaging.
Course Book: Bayesian Statistics: an introduction, Peter M. Lee, 4th Edition - Wiley