Course goals & objectives
This course introduces students to linear models and its extensions
for model building, including exploratory data analysis techniques,
variable transformations and selection, parameter estimation and
interpretation, prediction, hierarchical models, model selection and
Bayesian model averaging. The concepts of linear models will be
covered from Bayesian and classical viewpoints. Topics in Markov chain
Monte Carlo simulation will be introduced as required, however it is
expected that students have either taken STA 601 or are co-registered.
All students should be extremely comfortable with linear/matrix algebra and mathematical statistics at the level of STA 611 or equivalent; Statistical Inference - Casella and Berger is an excellent resource in case you need to review any mathematical statistics. If you need to review linear algebra, please explore material under Resources and links - Gilbert Strang’s online course is highly recommended.
The course goals are as follows:
- Understand the different philosophical approaches to statistical
analyses (Bayesian and frequentists)
- Build a solid foundation for the probability theory and inference for Gaussian
linear models and extensions.
- Build appropriate statistical models for data, perform data analysis
using appropriate software, and communicate results without use of
statistical jargon.
- Become familiar with reproducible research using github, RStudio, knitr and $\LaTeX$ to produce technical, literate data analyses.
Course Outline
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
- Formulation of Bayesian Inference
- Subjective and Default Priors
- Related Shrinkage Methods and Penalized Likelihoods (Ridge regression, lasso, horseshoe etc)
- Model Selection (comparison of classical and Bayesian approaches)
- Bayes Factors
- Bayesian Model Averaging
- Model Checking: Residual Analysis, Added-Variable Plots, Cooks-Distance Transformations
- Bayesian Outliers
- Bayesian Robust Methods for Outliers
- Generalized Linear Model and Weighted Regression
- Hierarchical Models
Please check the website for updates, slides and current readings.
Grading:
| Homework | 20% |
| Midterm | 25% |
| TakeHome | 25% |
| Final | 25% |
| Participation | 5% |
Grades may be curved at the end of the semester. Cumulative numerical averages of 90 - 100 are guaranteed at least an A-, 80 - 89 at least a B-, and 70 - 79 at least a C-, however the exact ranges for letter grades will be determined after the final exam. The more evidence there is that the class has mastered the material, the more generous the curve will be.
Homework:
These will be assigned weekly on the course webpage.
The objective of the problem sets is to help you develop a more in-depth understanding of the material and help you prepare for exams and projects. Grading will be based on completeness as well as accuracy. In order to receive credit you must show all your work.
No late assignments will be allowed, however the lowest score will be dropped.
You are welcomed, and encouraged, to work with each other on the problems, but you must turn in your own work. If you copy someone else’s work, both parties will receive a 0 for the problem set grade as well as being reported to the Office of Student Conduct. Work submitted on Sakai will be checked for instances of plagiarism prior to being graded.
Submission instructions: You will submit your HW on Sakai by
uploading a PDF. If the TAs cannot view your work, or read your
handwriting, you will lose points accordingly. We will be using R/knitr with $\LaTeX$ for preparing assignments using github classroom for data analysis.
Attendance & Participation:
You are expected to be present at class meeting and actively
participate in the discussion. Your attendance and participation
during class, as well as your activity on the discussion forum on
Sakai will make up 5% of your grade in this class. While I might
sometimes call on you during the class discussion, it is your
responsibility to be an active participant without being called on.
Takehome Data Analysis Problem
The objective of the TakeHome is to give you independent applied
research experience using real data and statistical methods. You will
use all (relevant) techniques learned in this class to analyze a
dataset provided by me.
Further details on the TakeHome will be provided as due dates approach.
Note that you must score at least 30% of the points on the TakeHome Exam in order to pass this class.
Exams:
There will be one midterm and one final in this class. See course info for dates and times of the exams.
You are allowed to use one sheet of notes (``cheat sheet”) on the
midterm and two for the final. This sheet must be no larger than 8 1⁄2 x 11,
and must be prepared by you. You may use both sides of the sheet
and can write as small as you wish.
Policies Regarding Homework:
No late Homework
The lowest HW score will be dropped automatically at the end of the semester
Late work policy for TakeHome Data Analysis: 10% off for each day late.
The final exam must be taken at the stated time. Please book flights accordingly!
There will be no Makeup exams; if you miss the midterm for any reason, your predicted grade given the other information from the class will be used to fill in the missing grade.
Regrade requests must be made within 3 days of when the assignment is returned, and must be submitted in writing. These will be honored if points were tallied incorrectly, or if you feel your answer is correct but it was marked wrong. No regrade will be made to alter the number of points deducted for a mistake. There will be no grade changes after the final exam.
Use of disallowed materials (textbook, class notes, web references, any form of communication with classmates or other persons, etc.) during inclass exams will not be tolerated. For the Take Home data analysis, students are limited to materials covered in class or course resources; no external queries or use of outside resources.
This will result in a 0 on the exam for all students involved, possible failure of the course, and will be reported to the Office of Student Conduct. If you have any questions about whether something is or is not allowed, please ask me beforehand.
Email & Forum (Piazza):
I will regularly send announcements by email through Sakai; please make sure to check your email daily.
Any non-personal questions related to the material covered in class, problem sets, labs, projects, etc. should be posted on
Piazza forum.
Before posting a new question please make sure to check if your question has already been answered. The TAs and myself will be answering questions on the forum daily and all students are expected to answer questions as well. Please use informative titles for your posts.
Note that it is more efficient to answer most statistical questions ``in person” so make use of Office Hours.
Students with disabilities:
Students with disabilities who believe they may need accommodations in this class are encouraged to contact the Student Disability Access Office at (919) 668-1267 as soon as possible to better ensure that such accommodations can be made.
Academic integrity:
Duke University is a community dedicated to scholarship, leadership, and service and to the principles of honesty, fairness, respect, and accountability. Citizens of this community commit to reflect upon and uphold these principles in all academic and non-academic endeavors, and to protect and promote a culture of integrity. Cheating on exams and quizzes, plagiarism on homework assignments and projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, violate the Duke Community Standard, and will not be tolerated. Such incidences will result in a 0 grade for all parties involved as well as being reported to the Office of Student Conduct. Additionally, there may be penalties to your final class grade. Please review the Duke’s Academic Dishonesty policies.
This course has achieved Duke’s Green Classroom Certification. The certification indicates that the faculty member teaching this course has taken significant steps to green the delivery of this course. Your faculty member has completed a checklist indicating their common practices in areas of this course that have an environmental impact, such as paper and energy consumption. Some common practices implemented by faculty to reduce the environmental impact of their course include allowing electronic submission of assignments, providing online readings and turning off lights and electronics in the classroom when they are not in use. The eco-friendly aspects of course delivery may vary by faculty, by course and throughout the semester. Learn more at http://sustainability.duke.edu/action/certifications/classroom/index.php.
