As part of a group, you will undertake a project on a topic of your choice related to probability. The project is an opportunity to show off what you’ve learned and demonstrate how you can master and describe a topic or paper not covered in the course. Your final output for this project will be: 1) a technical report and 2) an oral presentation delivered to the class.

The projects will involve the exposition of a more advanced topic in probability, along with some simulations and analytic results.
Your goal is to give a 10 minute presentation that introduces, motivates, explains then applies your topic in an accessible fashion. You can approach this time in a number of ways, but you should definitely plan to include some interactive work that the other students can engage with for part of your presentation. You’ll be graded on the presentation by me, while your peers will also review your presentation (oral plus handout). The report should flow from the presentation (and not involve much if any additional work). Items from the presentations will be included on the final exam.

Looking for ideas? Check out some of the following topics or material in the following (or talk to me):

  • Nuclear radiation as a Poisson process (from Jenna Smith)
  • The Dirichlet process and its applications
  • Particle Filters
  • Stochastic Geometry and Tessellations (see Okabe and Boots)
  • Copulas
  • Monte Carlo Integration (foundation, extensions, variance reduction)
  • Psychological aspects of probability (e.g., Kahneman and Tversky)
  • The probability theory of Edwin Jaynes
  • Exchangability and Subjectivism, the probability theory of Bruno de Finetti

Group Formation

You will work in a group of three students.


This project is deliberately open-ended: as stated before, the task is to use describe an interesting topic in probability in an expository manner. There are two main guidelines that must be followed:

  • Your project must be centered around accessible topics in probability.
  • Your project must tell the class something (there must be a clear take-home message).

In addition, the following guideslines are critically important:

  1. You must clearly cite and reference your sources.
  2. All project related correspondence after the rosters must cc all project members and include the subject line “MATH391-X” where “X” is the project letter that I will assign you. Including all project members and using this specific subject line is important to ensure that no one is out of the loop and that emails don’t get lost at busy times during the end of the semester. I can’t stress how important it is for you to follow these instructions: please be sure to double check before you email!



Your proposal is due by email before midnight on Monday, November 14th.

Prior to writing your initial proposal you should get together with your groupmates and brainstorm three or four ideas before coalescing around one idea. Be ambitious! Once you decide on a topic that interests you, think about what you would like to end up with as a final result—without worrying about how to get there. The topic is completely open to your choice, but keep in mind the guidelines listed above.

Your proposal should contain the following content:

  1. Group Members: List the members of your group
  2. Title: The title of your project
  3. Purpose: Describe the general topic/phenomenon you want to explore, as well some carefully considered questions that you hope to address. You should make an argument motivating your work. Why should someone be interested in what you are doing? What do you hope people will learn from your project?
  4. Simulation: What role, if any, will simulation/computing play?
  5. Questions: What questions, if any, you have.
  6. Sources: what sources will you be using? Please attach a pdf of a paper if you are using one or a URL for other resources on the web.


Each group will be submitting a draft of their handout (double sided pdf, may be color or black and white) by email before midnight on Friday, December 2.

In conjunction with your oral presentation, you should prepare a single 8-1/2 by 11 double-sided handout. Include your group letter, title of project, your names, date, and the class on the top of the handout. Your handout should summarize the points that you hope to make in your presentation, and provide some details that may be hard to capture.

The handout is intended to help you move quickly through your presentation, space for the audience to answer questions or fill in blanks, and provide a reference for students to leave with (remember that the material from the project presentations will be included on the final exam).


An effective oral presentation is an integral part of this project. One of the objectives of this class is to give you experience conveying the results of a technical investigation to a non-technical audience in a way that they can understand. Whether you choose to stay in academia or pursue a career in industry, the ability to communicate clearly is of paramount importance. The burden of proof is on you to convince your audience that what you are saying is true. If your audience (who may very well be less knowledgeable about mathematics and statistics than you are) cannot understand your results or their interpretations, then the technical merit of your project is irrelevant.

On either Dec. 5 or 7, your group will make a 10-minute oral presentation to the class. We will be running a very tight schedule. You should make (good) slides and think about how you might use the boards. Your goal should be to convey to your audience a clear understanding of your topic, along with a basic understanding of your project. You should not tell us everything that you did. After hearing your talk, each student in the class should be able to answer:

  • What was your project about?
  • Why is it important?

You should prepare slides for your talk. PowerPoint is fine, but you might also want to consider Google Presentation, RMarkdown slides, Beamer (\LaTeX), or alternative, non-linear presentation software like Prezi. If your project has any interactive elements, please demonstrate them for us!

You will need to submit your slides via email by the midnight before your presentation along with a pdf of a handout (front and back of a single piece of paper: color allowed), but you should also bring the slides on a flash drive as a backup.

Technical Report

Your report will be due by midnight on Friday, December 9. These should be emailed as .Rmd or .Rnw files.


Be sure to motivate your topic at the beginning of your write-up. You should try to hook the reader early on. Assume that your audience is a skeptical student who has stumbled across your work but has very little time to read it. Can you give them a reason to continue reading? A striking visualization or result can help.


You don’t need to follow a specific format in the write-up, but you should start with an introductory paragraph and finish with a conclusion. These paragraphs needs not follow the formal writing style that you would use in most other classes. Here, a colloquial style that is accessible to a lay reader is appropriate.

Nevertheless, your write-up should address the following questions:

  • Why should anyone care about this?
  • What is this project about?
  • What did you learn?

Consider this report the place where you are carefully and exhaustively go through the topics that you explored in your presentation. Any resources that you consulted in researching your topic should be referenced at the end of this document.