STAT 632-600: Bayesian Statistics Fall Semester, 2011 Professor: Jeff Hart Office hours: - Tuesday and Thursday, 1:30-3:00 p.m., or by appointment (459E Blocker)

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Syllabus

Announcements

• I encourage you to complete the online evaluation of this course. You can do so between now and December 8th. Instructions are given below.
  1. Log into http://howdy.tamu.edu
  2. Click on the eLearning link located on the top-right of the screen.
  3. Click on the link for STAT 632.
  4. Click on Assessments link to the left.
  5. The evaluation is titled Instructor Course Appraisal.

• Your final exam is Friday, December 9 from 3 to 5 p.m. It is comprehensive, covering all the class notes. Here are the formula sheets you'll be allowed to use on the exam. A practice exam is posted below.

• My office hours on Thursday, December 8 will be from 10:00 a.m. to 11:30 a.m.

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
• Model selection
• Model selection example
• More on our model selection example
• Intrinsic Bayes factors in model selection

Supplementary notes

• Jeffreys' scale for interpreting Bayes factors

• More on Example 11

• More on testing a point null hypothesis

• Conjugate priors are not unique.

• Completing the square for quadratic forms

• Link functions in the GLM

• 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.

• MCMC diagnostics.

• Approximating a posterior predictive density using MCMC output.

• The reversible jump method used in the example on pp. 353-374N is described in this paper: Brooks, S.P., Giudici, P. and Roberts, G.O. (2003). Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65 3-55.

• Application of the reversible jump method to another data set.

• The following paper concerns Bayesian nonparametric estimation of a density: Griffin, J.E. (2010). Default priors for density estimation with mixture models. Bayesian Analysis 5 45-64.

• Dirichlet process priors

Homework assignments