Syllabus
MATH/STAT 355: Statistical Theory
Course Overview
This course explores the mathematics and theory underlying many of the modern statistical applications you have encountered in previous coursework.
Learning Goals
Throughout the semester, we will focus on the following topics:
- estimation: understand and implement common estimation methods in a variety of settings and models
- specifically: maximum likelihood estimation, method of moments, least squares
- properties of estimators: evaluate properties of different estimators and understand why you might choose one type of estimator over another
- specifically: bias, variance, mean squared error, efficiency, sufficiency, consistency, asymptotic normality
- inference: understand the mathematical foundation of, and derive, techniques for using sample data to make generalizations, taking into account variability of estimates
- specifically: standard errors, confidence intervals, hypothesis testing
- as time allows, we’ll also explore special topics such as Bayesian statistics, theory of linear models, and more
- stay tuned!
In addition to these statistical theory concepts, this course also aims to help you develop general skills that are useful for future study and work in the field of statistics, including:
- communication: writing mathematical proofs, typesetting in LaTeX
- computing: conducting simulation studies
- collaboration: working effectively in a group setting
- ethical thinking: understanding the history of mathematical statistics and identify ethical issues associated with its application
- being comfortable working through challenges and mistakes
Schedule
This class will meet MWF, 9:40–10:40 am, in OLRI 254.
For a detailed daily schedule, check out the Schedule page on this website. Deadlines are also tracked in the MATH/STAT 355 Google Calendar.
This class will have a cumulative final exam. Our assigned final exam block is Saturday, May 9, 8:00–10:00 am. Save the date!
Instructional Team
Instructor
- Name: Dr. Kelsey Grinde (call me Kelsey or Professor Grinde)
- Pronunciation: kell-see grin-dee (listen here)
- Pronouns: she/her/hers
- Email: kgrinde@macalester.edu
- Office: OLRI 226
- Office Hours: Calendar
Welcome to Math Stat!
When I first started college (down the road at St. Olaf), I had absolutely no intention of taking a statistics course. But, in the spring of my sophomore year, I ended up taking Statistical Modeling on a whim. Much to my surprise, I loved it! The next fall, I took Statistical Theory, which ended up being a perfect course for a pure math major like myself with a new found interest in statistics. It was that class that helped me truly understand the motivation behind fundamental concepts like confidence intervals and p-values. And, it turned out to be fantastic preparation for grad school: during my first year in the Biostat PhD program at the University of Washington, my theory courses covered many of the same topics that I had seen in my undergraduate Statistical Theory course!
Math Stat is an exciting class because we get to dig deeper into the concepts you’ve seen in previous stats courses and show why we use the tools that we use. No matter your motivation, you belong in this class and I’m here to challenge and support you. If something about the course is not working for you, please let me know. I want all of you to have a positive learning experience in this course.
I’m looking forward to a great semester with all of you!
Kelsey
Preceptors
We are very lucky to have a fantastic preceptor who will be working with us this semester! Our preceptor will assist with grading, answer questions on Slack, and hold regular office hours.
- Name: Nick Kent
- Pronunciation: listen here
- Pronouns: he/him/his
- Major: Statistics
- Minors: Comp Sci, Econ
- Office Hours: Calendar
The role of an MSCS preceptor is to help students with content questions, assist in the navigation of available resources, advise on studying approaches for classes, and assist with concepts, tools, and skills needed for problem sets. Students are accountable for their own learning; as such, preceptors are not allowed to share answers to assignments (unless specifically directed by the instructor), are not expected to immediately know the right approach, or provide assistance outside of office hours. Additional guidelines and expectations on how to interact with preceptors can be found here: MSCS Preceptor Expectations.
Course Details
Materials
Course Website: You will access most materials for class (lecture notes, in-class activities and solutions, daily announcements, etc.) on this website.
Moodle: We will use Moodle primarily to post and submit assignments (checkpoints, problem sets).
Textbook: We do not have a required textbook for this course. Instead, I will frequently assign readings from the MATH/STAT 355 Course Notes developed by Macalester faculty. I may occasionally assign readings from other sources; all such readings will be free and made available to you via the course website or Moodle.
If you’re looking for a supplemental reading resource, check out the textbooks listed on the welcome page – many of these are available at the Macalester Library!
RStudio: We will not spend as much time in R this semester as you may be used to in other stats courses. However, we will still use it occasionally! At the start of the semester, please take some time to update your versions of R and RStudio. Instructions can be found here: R and RStudio Setup.
LaTeX: LaTeX is a document preparation system used to create high-quality scientific and technical communications. We will be using LaTeX to typeset homework assignments. It is freely available and can be used either within Quarto documents in RStudio, via a local TeX distribution, or via online editors like Overleaf. More info on getting setup here: LaTeX Resources.
Communication
I will primarily use Slack to communicate with you outside of class time. Click this link to join. Please get in the habit of checking regularly!
At the start of the semester, I highly recommend that you download the mobile app and/or desktop version of Slack and set up notifications in a way that will best help you stay up-to-date with any content posted there.
When YOU have a question…
- Stop by Office Hours! ( Kelsey | Preceptor )
- Use Slack to ask questions relevant to the entire class (content, homework, LaTeX, etc.)
- Use email (or Slack DM) to send personal questions/updates (attendance, accommodations, etc.) or to request a one-on-one appointment
I do my best to respond to messages quickly. However, I also try hard to maintain a healthy work/life balance. With that in mind, please allow extra time for a response on evenings and weekends!
Philosophy
Learn by doing. Our class time will be very active. A typical class session will include a short question and answer session in addition to a collaborative activity in which you will deepen your understanding of the statistical concepts. You will prepare for this work outside of class through a combination of readings, videos, and practice problems.
Please bring a notebook, writing utensil, and laptop with you to class each day.
Learn by making mistakes. Learning by doing will entail making mistakes. This is OK! Learning from those mistakes will form some of your most valuable learning experiences.
I have designed the grading system for this course with this growth mindset in mind—more info below.
Learn by collaborating. Working effectively in a group setting is an essential life skill that requires practice and demonstrably improves your learning (evidence). You will spend much of our class time working on activities with small groups.
If working with a specific person in this class would be a barrier to your learning, please let me know (no reason necessary!).
Old concepts in new light. This course is an opportunity for you to deepen your understanding of the concepts to which you were first introduced in STAT 155. We will take new understandings from probability theory and use them to better understand why some statistical methods are standard. We’ll also learn alternative approaches and see the commonality between different approaches. This will give you the ability to learn other advanced topics not covered in this course.
MATH/STAT 354: Probability is a strict prequisite for this course. If you have not yet completed that class, please let me know as soon as possible.
Theory with application. This course emphasizes mathematical theory in conjunction with application. Why?
- Theory helps to serve the application.
- Applications drive theory development.
- Understanding can come from a variety of activities (derivations, simulation, application to data).
Learning Activities & Assessments
Pre-Class Preparation. This course will operate under a partially “flipped” design. To prepare for class each day, you will be assigned readings, practice problems, and/or short pre-recorded lecture videos that you should complete before class. Most days, those assignments will be accompanied by a short Moodle checkpoint. The goal of these checkpoints is to assess which concepts need further discussion in class, and to help your long-term retention: the process of practicing information retrieval can help you more fully understand concepts (read Make it Stick to learn more!). See the Before section of the Schedule for details and deadlines.
In-Class Activities. During class time, you will frequently work in small groups on exercises that practice, apply, and/or extend topics covered in the assigned readings and lectures. Although you will not formally submit these activities, attendance and participation in these activities is expected and will be beneficial to your learning. Please see the attendance policy, below, for expectations around what to do if you ever have to miss class.
Problem Sets. For each unit, you will complete one problem set with problems that include derivations that apply course concepts in novel settings, proofs that extend and deepen your understanding, and questions that challenge you to conduct simulations to support your mathematical understanding. Problem sets will be typed, using LaTeX. These assignments will typically be due on Fridays, approximately every other week. See the After section of the Schedule for details and deadlines.
Quizzes and Exams. To assess individual understanding, there will be six quizzes and one final exam spaced throughout the semester:
- Quiz 1: Friday, February 13
- Quiz 2: Friday, February 27
- Quiz 3: Friday, March 13 (note: this is the last day of class before spring break. plan accordingly!)
- Quiz 4:
Friday, April 3Wednesday, April 8 - Quiz 5:
Friday, April 14Friday, April 24 - Quiz 6: Monday, May 4 (note: this is the last day of class!)
- Final Exam: Saturday, May 9, 8–10 am
Quizzes and exams will be completed during class time and will be closed notes. Opportunities for revision will be built into the structure of the quizzes, with two opportunities to demonstrate your understanding of each topic.
Grading
This course will use a non-traditional grading system, designed with the goals of aligning your grades with our course learning objectives, providing feedback to guide your learning, and allowing space to make and learn from mistakes.
To earn an A in this course, you must consistently demonstrate:
To earn a B: frequently meet almost all of these criteria, and show meaningful progress on all others
To earn a C: frequently meet some of these criteria OR meet many of the criteria but less often, and show progress toward a few others.
(+ and - grades will be awarded in intermediate cases)
The Final Exam will act as a grade modifier:
- If you score above a 90% on the final, I will bump your grade up one level (eg B -> B+).
- Note that Macalester does not give me the option to award an A+. Thus, students who earn an A according to the criteria above and score above 90% on the final will still be awarded an A. But I will write you a very strong letter of recommendation should you need one :)
- If you score between an 80% and 90%, your grade will remain the same.
- If you score between 70% and 80%, I will bump your grade down one level (eg B -> B-).
- Scores lower than 70% will drop grades even further (eg B -> C+). At minimum, you must take, and demonstrate genuine effort on, the final exam in order to earn a passing grade in the course.
More details, and resources to help you track your progress, will be provided in class. If you are ever concerned about your learning (or grade) in this class, please set up an appointment with me to discuss!
Course Policies
Academic Integrity
I expect you to be familiar with, and follow, the college standards on academic integrity: link. Review this policy if you haven’t done so recently.
I encourage you to form study groups early in the semester as a way to work with your classmates to discuss concepts and problem sets. In order for you to receive feedback on your learning, you must:
- submit your own work (code and writing)
- explicitly credit your sources (including AI, more details below)
I take academic integrity seriously and will schedule a meeting with you if I have concerns that this policy has been violated.
Accommodations
I am committed to creating an accessible and inclusive classroom for all students. If you need any accommodations, please contact the Center for Disability Resources to discuss your needs. Once you’ve met with them, please then set a time to meet with me to discuss your accommodation plan for this course. It is important to arrange this meeting as early in the semester as possible: if you wait until later, I will be unable to accommodate you retroactively.
Artificial Intelligence (AI)
AI can be a useful tool, when used thoughtfully. However, it is important to be aware of its limitations and to ensure you are not using it in a way that impedes your learning.
Some of the questions on your problem sets can be solved by AI tools or otherwise found online. However, relying too heavily on these tools will impede your learning and leave you ill-prepared for our in-class, closed-notes quizzes and exams. WHEN you get stuck on a problem, here’s what I recommend instead:
- review course materials and your own notes
- ask a friend, come to office hours, and/or post your question on Slack
- take a break and come back to it the next day
- repeat!
AI is not always correct. Even when correct, AI may use terminology or syntax that is inappropriate for our course. Never copy-paste output from AI into your assignment. Critically evaluate the response and rewrite it in your own words (or code) before submitting.
Any ideas, language, or code generated by AI must be cited, just like any other resource. Failure to do so is a violation of Macalester’s Academic Integrity Policy (see above). Check out these tips on how to cite AI: link.
The prompts you write, attachments you upload, etc. are providing data to the AI tool. Don’t provide data you don’t have permission to share. (Not sure? Ask me!)
Remember that AI has a large environmental impact (see here and here and here and here). If you can do something in a more energy efficient way (e.g. using the steps recommend above), please do!
Long story short, please be mindful of your use of AI and try to first use resources specific to our course (including your instructor and preceptor!) whenever possible. If you do use AI, make sure you cite it appropriately. I’ll provide space on problem sets for you to do so.
Attendance
You are warmly invited, encouraged, and expected to attend and participate in all class meetings. Participation means coming to class prepared, actively discussing material, engaging in the activities, and asking questions. This will be important not only for your own learning, but also for our ability to build a community and maintain a sense of connection and commitment to one another during the semester.
There may be times you are unable to attend class. You NEVER owe me personal information about your health or otherwise, but I appreciate a heads-up if you will be absent. Frequent absences will impact your learning (and your grade). I will reach out if I am concerned about your attendance/participation, and I encourage you to do the same.
- Check the daily schedule to find out what we’re doing in class that day.
- Review the notes and complete the in-class activity on your own.
- Check in with a friend in the class and/or come to office hours to ask any follow-up questions.
- Send me a quick email. Reminder: no details about the reason for your absence needed! I appreciate hearing from you and it helps keep communication lines open.
Extensions
Deadlines are social contracts that allow all stakeholders the ability to plan their work. I strive to facilitate a balance between providing quick feedback, managing workloads (for you, preceptors, and me), and being flexible wherever possible.
With that in mind…
Checkpoints: Except in exceptional circumstances, I will NOT grant extensions or accept late submissions for checkpoints. These assignments are important preparation for class.
Problem Sets: Problem Sets will typically be due at the start of class (in person!) on Fridays. If you are worried about meeting one of these deadlines, please email me to request an extension. Each student will automatically (no reason necessary!) be granted the use of three 3-day extensions for problem sets. These extensions apply to late submissions as well: if you miss the deadline, you can use one of your remaining extensions to submit three days later, without penalty.
Quizzes and Exams: If you have a conflict with a schedule quiz or exam date, please get in touch with me at least one week in advance for full consideration. I cannot guarantee that I will be able to accommodate all requests, but I will do my best to work with you in exceptional circumstances.
MSCS Community Guidelines
I expect you to be familiar with and adhere to the MSCS Community Guidelines in all of your interactions with classmates, preceptors, and instructors. This will include:
- Being inclusive
- Being present
- Asking for and offering help
- Being collaborative
- Being mindful of academic integrity
If you witness or experience any violations of these guidelines, I encourage you to come chat with me and/or follow the suggestions in the Community Guidelines document to report the issue.
Religious Observance
Students may wish to take part in religious observances that occur during this semester. I’ve done my best to schedule deadlines around major holidays, but if you have a religious observance/practice that conflicts with class or an assignment deadline, please let me know as soon as possible so we can discuss accommodations.
Title IX
If you or anyone you know has experienced harassment or discrimination on the basis of sex or gender, know that you are not alone. Macalester provides staff and resources to help you and support you. More information is available on the Title IX website.
Please be aware that all Macalester faculty and preceptors are mandatory reporters: if we become aware of incidents or allegations of sexual misconduct, we are required to share the matter with the Title IX Coordinator. Although we have to make that notification, you control how your case is handled, including whether or not you wish to pursue a formal complaint. If you’d like to speak to someone confidentially, see here.
Tips for Success
⏱️ Make Time
You will be asked to think, derive, compute, and write in this class. You will get stuck, run into errors, and practice the skill of troubleshooting. Start your problem sets early so that you have the opportunity to ask questions in office hours and space to work through challenging problems.
In addition to the 3 hours we spend together during our class meeting time, you should expect to spend on average about 7 hours per week on the academic and creative work related to class. If you find that you are spending considerably more (or considerably less!) time to engage with this course, please contact me so that we can determine the best course of action.
❓ Ask Questions
When you have questions, please stop me during class, ask your neighbor, post on Slack, and come to office hours. Saying I don’t understand is an important part of learning and it helps others.
Office hours are a great time to talk about course material and assignments, study strategies, selecting courses, declaring a major, grad school and/or career planning, or life. You don’t need to have a specific question in order to attend office hours: it can also be a great space to review concepts, talk through examples, or just chat!
✨ Prioritize Your Well-Being
Remember that beyond being a student, you are a human being carrying your own experiences, thoughts, emotions, and identities with you. It is important to acknowledge any stressors you may be facing, which can be mental, emotional, physical, financial, etc., and how they can have an academic impact.
During class time, eat when you are hungry, drink water, use the restroom, and step out if you are upset and need a break. Please do what is necessary so long as it does not impede your or others’ ability to be mentally and emotionally present in the course.
Outside of class time, sleeping, moving your body, and connecting with others can be strategies to help you be resilient at Macalester. If you are having difficulties maintaining your well-being, please don’t hesitate to contact me and/or find support from other resources.
As part of prioritizing your well-being (and that of others around you), it is important that you stay home if you are feeling sick. This is particularly meaningful to me as someone with a severely immunocompromised family member. I will happily work with you to get you caught up!
Questions?
Do you have questions about anything contained in this syllabus? Are you wondering about something that you can’t find here? Please reach out if so!