Main aims of Bayesian Statistics. Parametric inference, predictive inference. Observation processes, exchangeability. Univariate parametric models. Monte Carlo approximations. The normal model.Posterior approximation with the Gibbs sampler. The multivariate normal model. Group comarison and hierarchical modelling.Linear regression. Nonconjugate priors and Metropolis-Hastings algorithms. Linear and generalized mixed effect models. Methods for ordinal data.
Peter D. Hoff A First Course in Bayesian Statistical Methods, 2009 Springer
Learning Objectives
Knowledge: Deep understanding of Bayesian inference techniques. use of parametric models defining parameters as random variables
Prerequisites
Statistical inference
Teaching Methods
Oral lectures and exercise sessions
Further information
Some knowledge of the R software is required
Type of Assessment
There will be two intermediate written and a final oral examination
Course program
Law of total probaility and Bayes rule. Bayesian inference: notation. main differences between Bayesian and frequentist inference. Observation processes. Different hypotheses of dependence. Gaussian proces, mixture processes: Exchangeability.
Binomial model, HPD regions. predictive inference Conjugate families. Not informative priors, Jeffreys priors, Monte Carlo methods, AR and importance sampling. MCMC, Normal multivariate analysis, Regression methods and variables selection. hierarchical models, linear hyerarchical models Bayesian generalized linear models.