STAT 632-600: Bayesian Statistics Fall Semester, 2009 Professor: Jeff Hart Office hours: 3:00-4:00 p.m. Monday, Wednesday and Friday, or by appointment (459E Blocker)

This might be a picture of Thomas Bayes . Surf here to find out more about the picture.

Syllabus

Announcements

• Here are the R Aquilae data. In the first column are the standardized epochs and in the second the recorded periods.

• Project guidelines.

• Your project is due Wednesday, December 16.

• Please take the opportunity to evaluate this course. You may do so online as follows:
  • Log into howdy.tamu.edu.
  • Click on the eLearning link located on the top-right of the screen.
  • Click on the link for STAT 632.
  • Click on the Assessments link to the left.

  The evaluation is titled Instructor Course Appraisal. It will be available starting at 8 a.m. on November 21 and will conclude at 11:30 p.m., December 8th. There is no time limit for the evaluation as long as it is submitted prior to December 8th at 11:30pm.

Class notes

• Introduction
• Introduction to decision theory
• Example of selecting an optimal decision rule
• Initial and final precision and beginning of single-parameter models
• Bayesian analysis of a binomial experiment
• Prior distributions
• Bayesian credible regions and hypothesis testing, and examples in a normal model
• The posterior and sufficient statistics, and Bayes analysis of exponential data
• Example of inferring an exponential rate parameter, Poisson data, and testing a point null hypothesis
• Introduction to multiparameter models
• Multinomial data and multivariate normal distribution
• Multivariate normal data with both mean and covariance unknown
• Large sample properties of Bayesian inference
• Linear regression
• Conclusion of linear regression and beginning of generalized linear models
• Use of Newton-Raphson and Fisher scoring to obtain MLEs for generalized linear models
• Prior distributions for GLMs
• Bayesian computations and rejection sampling
• MCMC
• Convergence issues and canonical forms for proposal distribution
• Gibbs sampling and practical issues
• An example involving a variable star
• More on the variable star example
• Kernel density estimation
• Hierarchical models
• Hierarchical linear models

Supplementary notes

• Conjugate priors are not unique.

• Here is a paper that proposes methodology for fitting generalized linear models to correlated data: Liang, K.-Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 13-22.

• Read Section 2.2 of Multivariate statistical modelling based on generalized linear models by Fahrmeir and Tutz to learn more about efficacy of Fisher scoring and Newton-Raphson in finding MLEs of GLMs.

• Some more details in the proof on pp. 240N-242N.

• Here is a paper that analyzes data for a large collection of variable stars: Hart, J.D., Koen, C. and Lombard, F. (2007). An analysis of pulsation periods of long period variable stars. Journal of the Royal Statistical Society: Series C (Applied Statistics) 56 587-606.

• Approximating a posterior predictive density using MCMC output.

Homework assignments

• Assignment #1
  Due Friday, September 18

• Assignment #2: Exercises 14, 16, 17, 19, 23 in Chapter 2 of GCSR
  Due Friday, September 25
  
  Note: In Exercise 16(b), what you are asked to prove is true only for n>1.
  

• Assignment #3: Exercises 1, 3, 4, 10, 13 in Chapter 3 of GCSR
  Due Friday, October 2

• Assignment #4: Exercises 2, 3, 4 in Chapter 4 of GCSR and Exercise 1 in Chapter 14 of GCSR
  Due Friday, October 23

• Assignment #5
  Due Friday, October 30

• Assignment #6
  Due Monday, November 9

Homework solutions

• Homework #1 I graded the AIDS problem and Exercises 2.2 and 2.9. Point values were as follows:
  • AIDS problem: (a) and (b) were 7 apiece and (c) was 6.
  • 2.2: 15
  • 2.9: 15

• Homework #2 I graded Exercises 2.14, 2.16 and 2.17. Point values were as follows:
  • 2.14: 20 points
  • 2.16: 15 points
  • 2.17: 15 points

• Homework #3 I graded Exercises 3.3, 3.4 and 3.10. Exercise 3.4 was worth 20 points, and the other two were 15 apiece.

• Homework #4 I graded Exercises 4.2 and 4.3, which were worth 30 and 20 points, respectively.

• Homework #5 I graded both problems. The first and second were worth 20 and 30 points, respectively.

• Homework #6

Practice exams

• Here's a midterm exam from a previous 632 class. I won't rule out the possibility that some problems on your midterm will require calculations, but at least some of them will be similar to the ones on this 2008 midterm.
• Here's a solution to the 2008 midterm.
• Here's a practice exam for your second midterm.
• Solution to second practice exam.

Test solutions

• Midterm 1

• Midterm 2

Computer code

• R function for finding an HPD region for an exponential rate parameter.

• R function for logistic regression.

• R function for doing rejection sampling in a very specific case.