STA721: Linear Models (Fall 2024)
Course Description
This course introduces students to linear models and extensions for model building from the frequentist (OLS/MLE and penalized likelihoods) and Bayesian paradigms, with an emphasis on a geometric perspective. Course topics include optimal estimation and prediction, distributional assumptions and model checking, hypothesis testing and model selection including Bayes factors and intrinsic Bayes factors, and Bayesian Model Averaging. Students should have a strong background in matrix algebra and distribution theory. Co-requisite: STA 602L, 702L or equivalent.
Course Info
Textbooks
Textbook | Ordering Information |
---|---|
Plane Answers to Complex Questions Ronald Christensen (2011) 4th Edition Springer-Verlag, NY. The textbook is freely available as an eBook thru the Duke Library. You’re welcomed to read on screen or print it out. If you prefer a paperback version you can buy it at the cost of printing from Springer or purchase a hardback version at your favorite vendor. | |
Linear Regression Analysis, George A.F Seber and Alan J. Lee (2003) 2nd Edition, Wiley eBook in Duke Library. Duke Library is aware the link to the ebook is broken See the |
Canvas site for a pdf version until the links are fixed.
Lecture
Tuesday and Thursday
1:25pm - 2:40pm
Old Chemistry 123
Labs
Fridays
10:05am - 11:20pm
LINK 088 (Clasroom 4)
Final Exam
December 15
9:00am - 12:00pm
Old Chemistry 123
Instructional Team and Office Hours
Role | Name | Office Hours | Location | |
---|---|---|---|---|
Instructor | Dr Merlise Clyde | Tues 2:45 - 3:45 or by appointment |
223E Old Chem | |
TA | Bongjung Sung | Mon 9:30-11:30am | 203B Old Chem |
Course Topics
Course topics will be drawn (but subject to change) from
- Motivation for Studying Linear Models as Foundation
- Random Vectors and Matrices
- Multivariate Normal Distribution Theory
- Conditional Normal Distribution Theory
- Linear Models via Coordinate free representations (examples)
- Maximum Likelihood Estimation & Projections
- Interval Estimation: Distribution of Quadratic Forms
- Gauss-Markov Theorem & Optimality of OLS/GLS
- Formulation of Bayesian Inference
- Subjective and Default Priors
- Related Shrinkage Methods and Penalized Likelihoods (Ridge regression, lasso)
- Model Selection (comparison of classical and Bayesian approaches)
- Bayes Factors
- Bayesian Model Averaging
- Model Checking: Residual Analysis & Diagnostics
- Robust Methods for Outliers
- Generalized Linear Model
- Hierarchical Models
Please check the website for updates, slides and current readings.