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//**STAT 882: Nonparametric Bayesian Inference**//

**Winter Quarter 2009**

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\\ ^**Instructors:**| |**[[snm@stat.osu.edu|Steve MacEachern]]**.  | |office Hours: Friday 9:30 - 10:30am in 205C [[http://www.osu.edu/map/building.php?building=063|Cockins Hall]], and by appointment|
^ | |**[[xinyi@stat.osu.edu|Xinyi Xu]]**.  | |office Hours: Tuesday 9:30 - 10:30am in 440G [[http://www.osu.edu/map/building.php?building=063|Cockins Hall]], and by appointment|

\\ ^**Lecture Hours & Location:**| |TTh 1:30-2:48pm, [[http://www.osu.edu/map/building.php?building=280|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.\\ \\ 

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==== Course syllabus ====

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\\ ==== Announcements: ====

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

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\\ ==== Lectures: ====

  - //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.
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  - //Week 2:// From parametric Bayesian inference to nonparametric Bayesian inference. The constructions and properties of Dirichlet process. References: 
    * Ferguson, T.S. (1973). [[http://links.jstor.org/sici?sici=0090-5364%28197303%291%3A2%3C209%3AABAOSN%3E2.0.CO%3B2-U|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.)
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  - //Week 3:// Simple applications of Dirichlet process. Polya urn schemes. Sethuraman's representation. Posterior consistency. References: 
    * Ferguson, T.S. (1973). [[http://links.jstor.org/sici?sici=0090-5364%28197303%291%3A2%3C209%3AABAOSN%3E2.0.CO%3B2-U|A Bayesian Analysis of Some Nonparametric Problems]]. //The Annals of Statistics//, 1, 209-230.
    * Blackwell, D. and MacQueen, J.B. (1973). [[http://links.jstor.org/sici?sici=0090-5364%28197303%291%3A2%3C353%3AFDVPUS%3E2.0.CO%3B2-5|Distributions Via Polya Urn Schemes]]. //The Annals of Statistics//, 1, 353-355.
    * Sethuraman, J. (1994). [[Papers:Sethuraman|A constructive definition of Dirichlet priors]]. //Statistica Sinica//, 4, 639-650.
    * Ghosh, J. and Ramamoorthi, R. (2003). **Bayesian Nonparametrics**. Springer. (Chapter 1 and 4.)
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  - //Week 4:// Dirichlet process mixtures. Computational methods. References: 
    * Antoniak, C. (1974). [[http://links.jstor.org/sici?sici=0090-5364%28197411%292%3A6%3C1152%3AMODPWA%3E2.0.CO%3B2-6|Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems]]. //The Annals of Statistics//, 2, 1152-1174.
    * MacEarchern, S. (1998). [[Papers:MacEachern|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.
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  - //Week 5:// Computational methods for mixtures of Dirichlet process. References: 
    * MacEarchern, S. (1998). [[Papers:MacEachern|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:
    * [[Papers:MDPGibbsSampling|Handout]].   [[Data:R SmallWorkspace MDP model|Data]].   [[Codes:Basic MDP R code|Sample code]].
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  - //Week 6:// More on computational issues. Applications of Dirichlet process priors in Density estimation. References: 
    * Escobar, M. and West, M. (1995). [[Papers:EscobarWest|Bayesian Density Estimation and Inference Using Mixtures]]. //JASA//, 90, 577-588.
  - Example codes:
    * [[Papers:MDPGibbsSampling2|Handout]].   [[Codes:Modified Basic MDP R code|Modified Basic MDP R code]].   [[Codes:More Modified Basic R Code|More Modified Basic R Code]].
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  - //Week 7:// Applications of Dirichlet process priors in clustering/classification and regression problems. References: 
    * Medvedovic, M. and Sivaganesan, S. (2002). [[Papers:MedvedovicSivaganesan|Bayesian Infinite Mixture Models Based on Clustering of Gene Expression Profiles]]. //Bioinformatics//, 18, 1194-1206.
    * Lau J.W. and Green, P.J. (2007). [[Papers:LauGreen|Bayesian Model-Based Clustering Procedures]]. //Journal of Computational and Graphical Statistics//, 16, 526-558.
    * Quintana, F.A. (2006). [[Papers:Quintana|A Predictive View of Bayesian Clustering]]. //Journal of Statistical Planning and Inference//, 136, 2407-2429.
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  - //Week 8:// Applications of Dirichlet process priors in regressions (Cont.) An example of NP regression v.s. parametric regression: 
    * [[Handout:MDPRegression|Regression with NP Bayes models]].   [[Codes:MDP Regression R code|Sample codes]].   [[Handout:Regression2|A bit more analysis]].   [[Handout:ResidualDistns|Residual plot]].   [[Handout:PriorElicitation|Results of prior elicitation]].
  - References:
    * MacEachern, S.N. and Guha, S. [[Papers:MacEachernGuha|Parametric and Nonparametric Hypotheses in the Linear Model]]. Manuscript.

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//Last Update: Feburary 26, 2009.//