STA721: Linear Models (Fall 2024)

Photo of Neon Sign with Bayes Theorem.

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 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 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 Email 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.