We will cover the mathematical theory behind statistics. We will begin with a review of probability models and expectation, followed by: moment generating functions, the central limit theorem, and basic statistical inference. After that, we will review some linear algebra topics that are relevant in statistics before looking at applications including least squares regression and Markov chains. We'll finish the course looking at maximum likelyhood estimation, and Bayesian inference.
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 | Notes | Homework |
|---|---|---|---|---|
| 1 | Jan 13 - Jan 17 | Moment generating functions | Week 1 | |
| 2 | Jan 20 - Jan 24 | The Central Limit Theorem | Week 2 | HW1 |
| 3 | Jan 27 - Jan 31 | Transforming random variables | Week 3 | |
| 4 | Feb 3 - Feb 7 | Linear algebra review, Midterm 1 | Week 4 | HW2 |
| 5 | Feb 10 - Feb 14 | Linear regression | Week 5 | |
| 6 | Feb 17 - Feb 21 | Linear transformations | Week 6 | HW3 |
| 7 | Feb 24 - Feb 28 | Multivariate normal distributions | Week 7 | |
| 8 | Mar 2 - Mar 6 | Statistical inference, Midterm 2 | Week 8 | HW4 |
| 9 | Mar 16 - Mar 20 | Maximum likelihood estimation | ||
| 10 | Mar 23 - Mar 27 | Maximum likelihood estimation - con'd | ||
| 11 | Mar 30 - Apr 3 | Bayesian inference | ||
| 12 | Apr 6 - Apr 10 | Bayesian inference - con'd, Midterm 3 | ||
| 13 | Apr 13 - Apr 17 | Markov chains | ||
| 14 | Apr 20 - Apr 24 | TBA |
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% |
| Midterms | 30% |
| 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 three short midterm exams to test your understanding of the material. These exams will be announced in advance, and you will know exactly what concepts will be covered on each exam. You will not be asked to write proofs during these exams, 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?