lab:nonparametric_bayesian

**STAT 882: Nonparametric Bayesian Inference**

**Winter Quarter 2009**

^**Instructors:**| |**Steve MacEachern**. | |office Hours: Friday 9:30 - 10:30am in 205C Cockins Hall, and by appointment|

Xinyi Xu. | office Hours: Tuesday 9:30 - 10:30am in 440G Cockins Hall, and by appointment |

^**Lecture Hours & Location:**| |TTh 1:30-2:48pm, Baker Systems Engineering (BE) 134A |

**Text:** There is no required text book for this course. The lectures will be based on the instructors' notes and a collection of papers that will be handed out during the quarter.

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

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*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.

*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.)

*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.)

*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.

*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:
*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:
*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.

*Week 8:*Applications of Dirichlet process priors in regressions (Cont.) An example of NP regression v.s. parametric regression:- References:
- MacEachern, S.N. and Guha, S. Parametric and Nonparametric Hypotheses in the Linear Model. Manuscript.

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*Last Update: Feburary 26, 2009.*