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140.763 - Third Term 2006-7 BAYESIAN METHODS Instructor: Sining Chen Room: Wolfe Street Building W2300 (it is in the hallway with a lot of new
lockers, between the coffee shop and the courtyard, Behind a closed door with a sign
"classrooms W2300-W2304". Click here for a map) Time: Mon, Wed 1:30 - 2:50 pm Note that this course will only be
offered every two years. So the next time you can take it is
Spring 2009. |
Information on
this course on the school website may not be up to date. Please always use the
information on this page when there is a conflict of info.
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COURSE INFO |
* Prerequisites: Introduction to Statistical Theory I: 140.671. Some programming in R.
Please contact the instructor if you are not sure whether you should take this course.
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Instructor's Office Hour (tentative) Monday 3:00 - 4:00 pm W7033A
* Homework
due (tentative) Wednesday
before class
* Final
grades: 60% homework, 10%
participation, 30% final exam.
* Course
description:
Illustrates fundamentals
and current approaches to Bayesian modeling and computation in statistics.
Describes Bayesian approach to simple models, such as normal and binomial
distributions. Introduce concepts such as conjugate and noninformative prior
distributions. Use real data examples to illustrate tools including
hierarchical models (random effect models), hypothesis testing, model
averaging, linear regression, generalized linear models. Discusses modern
Bayesian computation: the implementation
and monitoring of Markov Chain Monte Carlo methods (Gibbs' sampler and
Metropolis Hastings algorithm).
* Course
learning objective:
Upon successfully
completing this course, students will be able to:
1) develop an
understanding and appreciation of the Bayesian approach;
2) specify models
and choose priors to adequately address a problem;
3) make posterior
inference: both algebraically and computationally.
1. Overview of the
course, grading policy, etc.
What
is Bayesian Statistics?
Single parameter model: the binomial model
HW1 [pdf]
2. Standard univariate models: the normal model, conjugate and noninformative prior distribution
3. Multiparameters models, normal with unknown mean and variance, the multivariate normal distribution, multinomial models.
HW2 [pdf]
4. Hierarchical models
5. The Stein estimator, shrinkage
HW3 [pdf]
6. Frequency Properties of Bayesian Inference;
Bayesian Hypothesis Testing
7. Posterior inference: Gibbs Sampling and Metropolis Algorithm: Re-analyses of the data sets below
READING ASSIGNEMENTS
*Sampling-Based Approaches to Calculating Marginal Densities by Gelfand A. and Smith A.F.M. JASA 1990 [pdf]
*Explaining the Gibbs Sampler by Casella G. and George E.I. The American Statistician 1992, vol 46, pp:167-174
*Understanding the Metropolis Algorithm by Chib S. and Greenberg E. The American Statistician 1995, vol 49, pp:327-335
*Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling by Gelfand A.E., Hills S.E., Racine-Poon A., Smith A.F.M., JASA, Vol. 85, pp. 972-985.
*A Generalization of the Probit and Logit Methods for Dose Response Curves Prentice P., Biometrics, Vol. 32, pp. 761-768. [ps]
8. Bayesian linear regression analysis, hierarchical linear regression models, Bayesian variable selection
9. Generalized linear models: hierarchical logistic regression, hierarchical log-linear regression, Bayesian Analyses of the rat tumor data
Variable Selection Via Gibbs Sampling George E.I. and McCulloch R.E. JASA Vol.88 pp. 881-889 [ps]
10. Bayesian model averaging
11. Topic of interest
12. Review
*Football scores and point spreads (Figure 1) [football.data]
*Speed
of Light measurements (Table 3.1) [light.data]
*Rat
Tumors (Table 5.1) [rat.data]
*Clinical
Trials of beta-blockers (Table 5.4) [betablockers.data]
*Baseball
batting (Table 6.1) [baseball.data]
*Congressional
Elections and incumbency (Section 8.4) [election.data]
*Forecasting
Presidential Elections Section 13.2) [forecast.data]
*Contingency
Table from a Sample Survey (Table 14.2) [cont_table.data]
*Cities
and Town in
*Rats:
a normal hierarchical model (BUGS Examples, Volume I and II) [rats.dat]
*Beetles
data set [beetles.dat]
*Finney's vasoconstriction data [vasoconstriction.dat]
*Posterior inferences under
a Binomial model [placenta.R]
*Posterior
inferences under a Poisson model [poisson.R]
*Posterior
inferences under a
*Sample
from a Multivariate Normal Distribution [multnorm.s]
*Sample
from a Wishart and Inverse Wishart Distributions [Wishart.R]
*Sample
from a Dirichlet Distribution [Dirichlet.R]
*Posterior
inferences under a
*Bayesian
Analysis of a Biossay Experiment [biossay.R] [commands.biossay.R]
*Estimating
the risk of tumor in a group of rats [tarone.R]
*Hierarchical
normal model with unknown variance: analysis of the diet measurements with a
Gibbs Sampling [hierarnorm.gibbs.R]
*Bayesian
Linear Regression Analysis of Radon Data [radon.R]
*Implement
Importance Sampling [importance.R]
*Approximating
the Posterior Distribution of all Unknown Parameters under a Hierarchical
Logistic Model: Estimating the risk of tumor in a group of rats [hlogistic.R]
*Implement
Metropolis [metropolis.R]
*Implement
a Gibbs Sampling [babymcmc.R]
*Implement
Gibbs Sampling under Bivariate
Required:
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Bayesian Data Analysis,
Second Edition (Texts in Statistical Science) by Andrew Gelman, John B. Carlin, Hal S. Stern, and
Donald B. Rubin (Hardcover - Jul 29, 2003) |
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Optional:
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Markov Chain Monte Carlo (Texts in Statistical Science
Series) by Dani Gamerman and Hedibert F. Lopes (Hardcover - May
10, 2006) |
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Statistical Decision Theory and Bayesian Analysis
(Springer Series in Statistics) by James O. Berger (Hardcover - Mar 25, 1993) |