Course description: Introductions to some advanced topics in statistical modeling and inference, including Bayesian hierarchical models, missing data problems, mixture modeling, hidden Markov models, Bayesian networks and additive modeling. The course will also cover some computational methods used and developed for these models and problems, such as the EM algorithm, data augmentation, the Gibbs sampler, dynamic programming, and belief propagation. Main topics includes:
(1) Bayesian hierarchical models, prior and posterior distributions, hyper-priors, posterior predictive distribution, shrinkage.
(2) Missing data problems, the EM algorithm, data augmentation, incomplete multivariate normal data.
(3) Mixture modeling, clustering algorithms, Dirichlet process.
(4) Hidden Markov models, dynamic programming, forward summation and backward sampling, Kalman filter.
(5) Bayesian networks, graphical model, DAGs, belief propagation, structural inference, model selection and model averaging.