ST 740-001:
Bayesian Inference and Analysis
Fall Session, 2007


Course:

ST 740-001 Bayesian Inference and Analysis

Time:

MWF from 10:15 a.m. to 11:05 a.m.

Place:

208 Patterson Hall
. .

Instructor:

Sujit Ghosh

Email:

ghosh@stat.ncsu.edu

Telephone

515-1950

Office:

220C Patterson Hall

Office hours:

Wednesday, 3:00-5:00 or by appointment

. .

TA:

Dhruv Sharma

Email:

dbsharma@stat.ncsu.edu

Telephone:

513-2956

Office:

Statistics Tutorial Center, 009 Patterson Hall

Office hours:

Tue 3:00 - 5:00

Class links: Course organization| Ask a question | Private tutors

Course prequisite: ST 522

Required text: Robert C. P. (2001). The Bayesian Choice, 2nd Edition. Springer Texts in Statistics. (ISBN: 0-387-95231-4)

Statistical resources: Bayesian Java Applications

Homework: Homework will normally be assigned weekly (as indicated on the homework page) at the end of class each Wednesday. Homework solution will normally be discussed in class on Fridays. The final homework average will be computed after dropping the two lowest grades.

Project: Project will be assigned after the midterm exam (as indicated on the project page). Students will be required to work in groups of size at most three members in a group. As part of the project students will be required to obtain a set of real data, formulate suitable models and fit models using techniques learned in this course (e.g., the use of softwares like R or WinBUGS is highly encouraged). Students are required to present the project in a mini seminar style within a time slot of no more than 15 minutes. Each member of a group will receive equal credit.

Examinations: The midterm examination will be closed book and closed notes held in class. However students will be permitted to bring one 8 1/2 by 11 inch sheet of notes (may use both sides) to the midterm exam. Students may bring calculators to the midterm exam, in addition to pen/pencil and scratch papers. There will be no in-class final exam. The project will be used as final exam.

Exam schedule:
Midterm exam
Monday, October 8
05:00-07:00 p.m.
In-class
Chapters 1-3
Final exam
Wed & Fri, December 5, 7
Time: TBA
In-class
Project presentations

Asking questions: If you have questions about lectures, homework assignments, exams, procedures or any other aspect of the course please log onto http://courses.ncsu.edu/, follow the links to "ST" and "ST740" and click on "Message Board". Then click on "Post New Topic", enter your question in the Message box, and click on "Submit Message". You will receive a response from me or another student. Everyone in the class will be able see your question and the response.

Anonymous mail: If you wish to send me an anonymous suggestion or reminder, send email to st740-001-sup@wolfware.ncsu.edu or just click here. The system will remove mail headers, but you must remember to remove your signature and other identifying information.

Grading system: Final grade will be based on:

Final Semester Score = (2.5xHW + 3.5xM + 4xF)/10

where HW is the homework average (out of 100) after dropping the two lowest scores and M, and F are the scores (out of 100) on the midterm, and final exam, respectively. Grades will be assigned on the +/- scale.

Auditing:Auditors are expected to attend class regularly and submit homework on the same schedule as the other students. The final grade for auditors (AU or NR) will be based on their final homework average. A homework score of 75 or better is required for an AU.

Policy on incomplete grades and late assignments: Unexcused late homework will not be accepted. HWs are to submitted by 5:00PM on the due date. If the midterm exam is missed, no substitute exam will be given. However, if there is a legitimate reason (as determined by the instructor) for missing the midterm exam, the final exam (project) will count 65% and the remaining 10% will be lost from the final semester score. Final exam can not be missed.

Policy on academic integrity: The University policy on academic integrity can be found in Code of Student Conduct Policy (POL11.35.1). For a more though elaboration see the NCSU Office of Student Conduct website. For this course group work on homework and project is encouraged. However copying someone else's work and calling them your own is plagiarism, so the work you turn in should be your own. Students are required to sign the Honor Pledge while submitting the assignments.

Students with disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1)

Online Class Evaluation: Online class evaluations will be available for students to complete during the last two weeks of class (November 26-December 9). All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.
Click Online evaluation. More information at ClassEval

Reference material (Have requested these be on reserve at DH Hill Library):

Bernardo, Jose M. and Smith, Adrian F. M. (2000). Bayesian Theory, Paperback edition. John Wiley & Sons Inc.

Bolstad, William M. (2004). Introduction to Bayesian Statistics. John Wiley & Sons Inc.

Carlin, Bradley P. and Louis, Thomas A. (2000). Bayes and Empirical Bayes Methods for Data Analysis, Second Edition. Chapman & Hall, CRC Press.

Congdon, Peter (2003). Applied Bayesian Modelling. John Wiley & Sons Inc.

DeGroot, Morris, H. and Schervish, Mark, J. (2001). Probability and Statistics, 3rd Edition. Addison Wesley.

Gelman Andrew, Carlin, John B., Stren, Hal S. and Rubin, Donald B. (2003). Bayesian Data Analysis, Second Edition. Chapman & Hall, CRC Press.

Robert, Christian P. and Casella, George (2005). Monte Carlo Statistical Methods, Second Edition, Second Printing. Springer Texts in Statistics.

Course objectives:

A prime objective of the ST740 course is to present techniques and basic results of theory and application of Bayesian inference at a rigorous and advanced calculus level.

In ST740 we develop the probabilistic language and computational tools of Bayesian statistics. The course describes probabilistic models for specifying prior distributions, summarizing posterior information, evaluating predictive distributions, formulating hierachical models and asymptotic consistency and asymptotic normality of posterior distributions.

In addition, the theory of estimation, credible regions, hypothesis testing, and prediction for common parametric models are unified into a decision theoretic framework and properties of estimators are investigated.

Students taking the course will have completed three semesters of calculus and had some exposure to basic probability and statistics. ST522 is a prerequisite for this course. A follow-up sequence, ST810B, presents similar materials from a nonparameteric perspective at the advanced measure-theoretic level.

Syllabus: In ST740 we shall cover most, but not all of the material in chapters 1 through 6 of Robert. If time permits, parts of chapter 7 and 10 will also be covered.
  1. The Bayesian paradigm: axiomatic foundations, conditional probability, prior and posterior distributions.
  2. Prior Information to Distriburion: sujective priors, maximum entropy priors, parameteric approximations, conjugate priors and noninformative priors.
  3. Decision Theory: action space, loss functions, minimaxity, admissibility and Bayes estimators.
  4. Point Estimation: MAP estimators, restricted parameter space, precision of Bayes estimators, predictions and Bayesian normal linear models.
  5. Tests and Credible Regions: Bayes factors, point-null hypothesis, pseudo bayes factors, credible intervals, HPD regions.
  6. Bayesian Calculations: numerical integration, analytic approximations, monte carlo methods, MH algorithm, Gibbs sampling, slice sampling and related MCMC methods.
  7. Hierarchical and Empirical Bayes: conditional decompositions, computational issues, optimaility of HB estimators, parameteric and nonparametric empirical Bayes alternatives.
(roughly two weeks will be devopted to each of the above topics)

Last updated on: October 05, 2007