Announcements:

• Homework 1 (both parts) will be due on Thursday, Jan. 22.

Lectures:

1. Week 1: Introduction to nonparametric Bayesian methods. Motivating examples. Consistency, false consistency, and principle driven modelling.

   References:

   • Berger, J.O. (1982). Statistical Decision Theory and Bayesian Analysis, 2nd edition. Springer-Verlag: New York.
   • Savage, L.J. (1954). The Foundations of Statistics. Wiley: New York.

2. Week 2: From parametric Bayesian inference to nonparametric Bayesian inference. The constructions and properties of Dirichlet process.

   References:

   • Ferguson, T.S. (1973). A Bayesian Analysis of Some Nonparametric Problems. The Annals of Statistics, 1, 209-230.
   • Ghosh, J. and Ramamoorthi, R. (2003). Bayesian Nonparametrics. Springer. (Chapter 3.)

3. Week 3: Simple applications of Dirichlet process. Polya urn schemes. Sethuraman's representation. Posterior consistency.

   References:

   • Ferguson, T.S. (1973). A Bayesian Analysis of Some Nonparametric Problems. The Annals of Statistics, 1, 209-230.
   • Blackwell, D. and MacQueen, J.B. (1973). Distributions Via Polya Urn Schemes. The Annals of Statistics, 1, 353-355.
   • Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4, 639-650.
   • Ghosh, J. and Ramamoorthi, R. (2003). Bayesian Nonparametrics. Springer. (Chapter 1 and 4.)

4. Week 4: Dirichlet process mixtures. Computational methods.

   References:

   • Antoniak, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics, 2, 1152-1174.
   • MacEarchern, S. (1998). Computational Methods for Mixture of Dirichlet Process Models. In Dey, Dipak D., Muller, Peter, and Sinha, Debajyoti (Eds.) Practical Nonparametric and Semiparametric Bayesian Statistics, 23-44. New York: Springer.

5. Week 5: Computational methods for mixtures of Dirichlet process.

   References:

   • MacEarchern, S. (1998). Computational Methods for Mixture of Dirichlet Process Models. In Dey, Dipak D., Muller, Peter, and Sinha, Debajyoti (Eds.) Practical Nonparametric and Semiparametric Bayesian Statistics, 23-44. New York: Springer.
   Example codes:
   • Handout.   Data.   Sample code.

6. Week 6: More on computational issues. Applications of Dirichlet process priors in Density estimation.

   References:

   • Escobar, M. and West, M. (1995). Bayesian Density Estimation and Inference Using Mixtures. JASA, 90, 577-588.
   Example codes:
   • Handout.   Modified Basic MDP R code.   More Modified Basic R Code.

7. Week 7: Applications of Dirichlet process priors in clustering/classification and regression problems.

   References:

   • Medvedovic, M. and Sivaganesan, S. (2002). Bayesian Infinite Mixture Models Based on Clustering of Gene Expression Profiles. Bioinformatics, 18, 1194-1206.
   • Lau J.W. and Green, P.J. (2007). Bayesian Model-Based Clustering Procedures. Journal of Computational and Graphical Statistics, 16, 526-558.
   • Quintana, F.A. (2006). A Predictive View of Bayesian Clustering. Journal of Statistical Planning and Inference, 136, 2407-2429.

8. Week 8: Applications of Dirichlet process priors in regressions (Cont.)

   An example of NP regression v.s. parametric regression:

   • Regression with NP Bayes models.   Sample codes.   A bit more analysis.   Residual plot.   Results of prior elicitation.
   References:
   • MacEachern, S.N. and Guha, S. Parametric and Nonparametric Hypotheses in the Linear Model. Manuscript.