We will cover the mathematical theory behind statistics. We will begin with a review of probability models and expectation, followed by: limit theorems, inference, linear models (regression and ANOVA), maximum likelyhood estimation, and Bayesian inference. If time permits, we will also study Markov chains and Monte Carlo methods.
The schedule below is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.
| Week | Dates | Topic | Homework |
|---|---|---|---|
| 1 | Jan 15 - Jan 19 | Covariance | HW 1 |
| 2 | Jan 22 - Jan 26 | Moment generating functions | HW 2 |
| 3 | Jan 29 - Feb 2 | Limit theorems | HW 3 |
| 4 | Feb 5 - Feb 9 | Normal distribution theory | HW 4 |
| 5 | Feb 12 - Feb 16 | Statistical inference | |
| 6 | Feb 19 - Feb 23 | Inner products & orthogonality, Midterm 1 | Midterm 1 |
| 7 | Feb 26 - Mar 2 | Linear regression | HW 5 |
| 8 | Mar 12 - Mar 16 | Analysis of variance | HW 6 |
| 9 | Mar 19 - Mar 23 | Maximum likelihood estimation | HW 7 |
| 10 | Mar 26 - Mar 30 | Bayesian inference | HW 8 |
| 11 | Apr 2 - Apr 6 | Bayesian inference - con'd | |
| 12 | Apr 9 - Apr 13 | Bayesian inference - con'd, Midterm 2 | Midterm 2 (tex) |
| 13 | Apr 16 - Apr 20 | Markov chains | |
| 14 | Apr 23 - Apr 27 | Markov chains | HW9 |
Attendance in this class is required. Repeated absences may result in a forced withdrawal from the course. You are responsible for any material you miss due to absence. Please let me know ahead of time if you know that you will not be able to attend class.
The term grade will be based on the following factors.
| Component | Proportion |
|---|---|
| Homework | 40% |
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final Exam | 30% |
I will assign homework problems every day in class. When the problems are due, I will collect them, but I will also ask you to present some of the solutions in class. Late homework submissions will only be allowed if you present your partial solutions in class! You are allowed to work together on the homework, but your final submissions must be your own work.
Each homework problem will be graded on a simple two point scale:
Your letter grade for homework will be determined by the percent of possible points you have completed.
There will be two in-class midterm exams. These midterms will be announced in advance, and you will know exactly what concepts will be covered on each midterm. You will not be asked to write proofs during the midterms, instead the midterms will focus on definitions, concepts and knowledge about probability.
There will be a cumulative final exam. It will include questions similar to the ones on the midterms, as well as a few more challenging problems similar to the ones on the homework.
In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations. How does this look?