Textbook

I teach from my notes, not from a textbook. The material I cover follows the Hoff text fairly closely, but the Hoff text is not as readable as I would like. Most students like to have a text as a supplement to my notes. The first two listed texts have electronic versions available from the library.

Primary text (recommended): This book, published in 2009, provides about the right level of coverage and is a reasonably up-to-date treatment.  An electronic edition of this book is available to George Mason University students and faculty from the university library. Computer code is available for most of the examples in the book.

Hoff, Peter D., A First Course in Bayesian Statistical Methods. Springer, 2009.

Secondary text (recommended):  This recently published book was written primarily for social scientists.  It is accessible, well-written, and gives a comprehensive treatment beginning from the very basics through sophisticated hierarchical Bayesian models. An electronic edition of this book is available to George Mason University students and faculty from the university library. Computer code is available at the github site for most of the examples in the book.

Reference text (recommended): This comprehensive text has become the standard reference in Bayesian statistical methods. The hyperlink below contains reviews, exercises, data sets and software. 

Gelman, A., Carlin, J., Stern, H., Dunson, D. B., Vehtari, A. and Rubin, D., Bayesian Data Analysis (3rd edition). CRC Press, 2013.

Supplemental text (recommended):  This recently published book provides comprehensive coverage of computational Bayesian statistics with a focus on conducting Bayesian analyses of real data sets.  The range of topics covered is much more extensive than the Hoff text, and will serve as a useful supplement for readers interested in Bayesian treatment of topics not covered in this course, such as generalized linear models, capture-recapture experiments, time series and image analysis.   R code and a solution manual are available.

Software

• Some of the homework and exam exercises can be managed with a full-featured spreadsheet package such as Microsoft Excel.  Others require more power.
  
• We will use R, a powerful (free) statistical graphics and computing language, and JAGS, an open-source, cross-platform engine for Bayesian data analysis that can be accessed from within R. Many of the exercises will require programming. RStudio is an integrated development environment for R. Some students prefer Python to R. You may use your preferred software as long as your solution is clear and I can understand what you did, but the solutions and examples will all be in R.
  

Prerequisites

• The formal listed prerequisite is OR 542 or STAT 544 or STAT 554 or equivalent.
• The real prerequisites are: 
• Experience with elementary data analysis such as scatterplots, histograms, hypothesis tests, confidence intervals, and simple linear regression. 
  
• A calculus-based probability course - elementary probability theory, discrete and continuous probability distributions, probability mass and probability density functions, cumulative distribution functions, common parametric models such as the normal, binomial and Poisson distributions.
• Experience with a high-level programming language. We will use R, a programming language for data analysis, and JAGS, a language for specifying and performing inference with Bayesian models.
• Comfort with mathematical notation.  We will not do proofs, but you will be expected to be comfortable following and doing mathematical derivations.
  

Requirements

Grades will be based on the following:

Policies and Resources

Schedule

The topics are listed below, along with readings from the Hoff text.  The take-home midterm exam will be posted by March 1 and will be due on Monday, March 20. The exam will include all material  covered up to and including March 6.  The final exam will be due on Monday, May 15 at 11:59 PM. The final exam will be cumulative. 

Unit 1	A Brief Tour of Bayesian Inference and Decision Theory	Week 1	Hoff, Chapter 1
Unit 2	Random variables, Parametric Models and Inference from Observation	Weeks 2-3	Hoff, Chapter 2
Unit 3	Bayesian Inference with Conjugate Pairs: Single Parameter Models	Weeks 3-5	Hoff, Chapter 3
Unit 4	Introduction to Monte Carlo Approximation	Weeks 5-6	Hoff, Chapter 4
Unit 5	The Normal Model	Week 6-7	Hoff, Chapter 5
Unit 6	Markov Chain Monte Carlo	Week 8-9	Hoff, Chapters 6 and 9
Unit 7	Hierarchical Bayesian Models	Week 10-11	Hoff, Chapter 8
Unit 8	Bayesian Regression	Week 12	Hoff, Chapter 9
Unit 9	Multinomial Distribution and Latent Groups	Week 13	Readings
Unit 10	Hypothesis Tests, Bayes Factors, and Bayesian Model Averaging	Week 14	Hoff, Chapter 10