This course considers data analysis based on probabilistic models. In particular, various methods of Bayesisan analysis are covered from basics to advanced machine learnings.
Content
· Introduction to Bayesian statistics
· Distributions
· Prior and posterior
· Markov Chain Monte Carlo
· Regression models
· Hierarchical models
· Model selelction and model assessment
· Finite mixture models
· Topic model
· Gaussian process prior
· Dirichlet process prior
· Advanced topics in Bayesian machine learnings
Textbooks
· Lecture slides found in the course web site.
· Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A. and Rubin, D. (2013). Bayesian Data Analysis. (3rd edition). CRC Press.
· PDF and additional materials are available at http://www.stat.columbia.edu/~gelman/book.
· Supplementary materials: [BER] – Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis. (2nd edition). Springer.