Stats 201C Advanced Modeling and Inference
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.
Link to the course Moodle site for lecture notes, homework assignments, etc.
References
1) Gelman, A. et al. Bayesian data analysis.
(Second edition, 2004).
2) Schafer, J.L. Analysis of incomplete
multivariate data. (First edition1997)
3) Rabiner, L.R. (1989) A tutorial on hidden Markov
models and selected applications in speech recognition. Proceedings of the IEEE,
77: 257-286.
4) Pearl, J. Causality: Models, Reasoning and Inference. (2000) UK: Cambridge
University Press.