Bayesian Modeling and Inference

General Information:

Instructor: Professor Bahman Moraffah
Office: GWC 333
Email: bahman.moraffah@asu.edu

Course Description:

Bayeisan approches provide flexible frameworks including prediction and estimation. As number of data sets grow, Bayesian nonparameteric modeling provides a more accurate model to cluster data. In this course, we discuss the Bayeisan inference and methods to do inference in high dimensional datesets.

Syllabus:

• Introduction to Bayesian theory and inference, de Finetti theory

• Markov chain Monte Carlo methods including Gibbs sampler, Hamiltonian Monte Carlo

• Varitional Bayes methods and stochastic variational Bayes

• Mixture models

• Dirichlet process and its construction methods, Polya urn, Chinese restaurant process, stick-breaking process

• Consistency and contraction rate in Bayesian nonparametric models

• Latent Dirichlet allocation and hierarchical Dirichlet process

• Two-parameter Poisson-Dirichlet process (Pitman-Yor process)

• Feature allocations, Beta process, Indian buffet process

• Gaussian Processes

• Combinatorial stochastic processes

Useful References

1. Bayesian Theory, Adrian Smith and José-Miguel Bernardo, 1994

2. Bayesian Nonparametrics, Nils Lid Hjort, Chris Holmes, Peter Müller, Stephen G. Walker, 2010

3. Bayesian Nonparametrics, Jayanta K. Ghosh, R. V. Ramamoorthi, 2003

4. Lecture Notes on Bayesian Nonparametrics, Peter Orbanz, Columbia University, 2014

5. Bayesian Nonparametrics, Micheal I. Jordan, Yee Whye Teh, 2016

6. Monte Carlo Statistical Methods, Christian P Robert and George Casella, second edition, 1999

7. Introducing Monte Carlo Methods with R, Christian P Robert and George Casella, 2009

8. Information Theory, Inference and Learning Algorithms, David J. C. MacKay, 2003