IN 132 and online

Monday 4:30-7:10 PM

Instructor: Kathryn
Blackmond Laskey

email:
klaskey@gmu.edu

web: http://www.seor.gmu.edu/~klaskey

phone: 703-993-1644

Office hours: Mondays 3:00 to 4:00 PM (online or in person), Wednesdays 4:00 to 5:00 PM (online only) or by appointment

Office location: ENGR 2214

Prerequisites:
web: http://www.seor.gmu.edu/~klaskey

phone: 703-993-1644

Office hours: Mondays 3:00 to 4:00 PM (online or in person), Wednesdays 4:00 to 5:00 PM (online only) or by appointment

Office location: ENGR 2214

OR 542 or
STAT 544 or STAT 554 or equivalent (a strong grounding in
probability with calculus; skill in elementary data analysis;
basic programming skills)

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 at the link below 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.

Marin, Jean-Michel and Robert, Christian, *Bayesian
Essentials with R *(2nd edition).* *Springer,
2014.

Alternate text

- Some of the homework and exam exercises
can be managed with a full-featured spreadsheet package such
as Microsoft Excel. Otheres 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 in R. 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.

- 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.

Grades will be based on the following:

Midterm exam (take-home) 35%

Final exam (take-home) 35%

**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 2 and will be due
on Monday, March 21. The exam will include all material covered
prior to March 14. The final exam will be due on Monday,
May 16 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 |