topics in probability for statistics

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course website for ubc stat 547c fall 2021 (Winter Term 1)

Syllabus

Description: A graduate-level course in probability with an emphasis on the basic tools that are applied in statistical science and related areas. The course will cover some basic measure theory as required (though less than in previous versions of the course): the axioms of probability and the construction of probability measures, random variables, and Lebesgue integration. From there, topics such as independence, characteristic functions, convergence, and conditional expectation/probability will take us from classical probability and statistics into more modern material.

Note that this course will have far less emphasis on measure theory than in previous years.

Pre-requisites: Ideally, one upper-division undergraduate course in probability and one in analysis. More details and some references can be found here (If you’re not sure, come talk to me after one or two lectures.)

Class meetings: Monday/Wednesday 12:30 - 2:00 pm. The first month of class meetings will be online (Zoom info available on Canvas); I am hopeful/optimistic for in-person meetings resuming after Thanksgiving. Class meetings will be recorded and posted to Canvas.

Instructor: Ben Bloem-Reddy

TA: Saif Syed - Email: saif dot syed at stat dot ubc dot ca - Office hours: TBD

Communications

Please use the email listed above for course-related communications.

Policy on concessions

If circumstances arise that prevent you from attending class or completing an assignment, please let me know as soon as possible. UBC’s policy on academic concessions is here. If you have grounds for academic concession, we will work together to find something that works.

The default policy for assignments: you have two “late days” to be used at your discretion during the term. When you have run out of late days, any further late days will result in the grade of the late work to be multiplied by 0.75 each day that it is late. If you are using a late day, you must let me know before the assignment is due.

The default policy for exams: except in very special circumstances, make-up exams will not be offered. In the case that you miss an exam, its contribution to your overall grade will be redistributed to the other exam(s). If you miss all exams, you will not be given a passing grade; depending on the circumstances other concessions may be available (e.g., late withdrawal).

Statement on UBC’s values and policies

UBC provides resources to support student learning and to maintain healthy lifestyles but recognizes that sometimes crises arise and so there are additional resources to access including those for survivors of sexual violence. UBC values respect for the person and ideas of all members of the academic community. Harassment and discrimination are not tolerated nor is suppression of academic freedom. UBC provides appropriate accommodation for students with disabilities and for religious and cultural observances. UBC values academic honesty and students are expected to acknowledge the ideas generated by others and to uphold the highest academic standards in all of their actions. Details of the policies and how to access support are available here: https://senate.ubc.ca/policies-resources-support-student-success.

Course objectives

This course is a foundation that will prepare you to:

Knowledge: language and mathematical foundations of probability as it is used in modern statistics, machine learning, and related fields.

Skills: techniques for analyzing probabilistic problems; technical tools for proving relevant properties.

Learning activities

Class meetings (via Zoom) will be our primary mode of interaction. However, most of your learning will occur outside of class through (see below for details on each):

Class meetings

Monday/Wednesday 12:30 - 2:00 pm. The first month of class meetings will be online (Zoom info available on Canvas); I am hopeful/optimistic for in-person meetings resuming after Thanksgiving. (Please read the in-person class info in anticipation of this.) Class meetings will be recorded and posted to Canvas.

You are expected to do all reading (textbook and/or notes) prior to class; I will cover certain important results in detail and devote time to examples. We will also use Zoom breakout rooms for short in-class exercises.

Reading

Textbooks

Primary textbook: J. Jacod and P. Protter, Probability Essentials, available as a PDF through the UBC library

Complements and references:

Assessment

If I had my way, all assessments would be formative. However, the university (and others) require summative assessments (i.e., your final grade). Your final grade will be calculated as follows:

Category Contribution Notes
Learning logs 10% See description below
Assignments 40% (roughly) weekly assignments; see description below
Midterm 25% See description below
Final 25% Project and final reflection; more details to follow

My primary concern is that you learn probability theory to the level of the course objectives. If you work hard and demonstrate what you are learning (via assignments, learning logs, in-class participation, office hours attendance, etc.), you will do fine.

Learning logs

Often, we don’t take the time for self-reflection during a course. This amounts to wandering through a forest without keeping track of where you’ve been and where you’re going. (Which can be nice, but can be harmful when trying to learn.) Especially when trying to learn conceptually/technically challenging material, I have found it helpful to step back to assess my understanding (or lack thereof).

To this end, I ask that you regularly reflect on your efforts and progress in a weekly learning log. At the end of each week, you will upload to Canvas a PDF file in which you reflect on your efforts, progress, and challenges over the week. These are a way to keep track of your learning and to keep in touch with me throughout the course. Grading will be binary (0 = no submission; 1 = submission) and count towards your final grade. Feel free to discuss with classmates in order to get started.

If you’re putting in the work, it will be clear here. If you’re struggling with something, writing it out can help clarify where you’re stuck and what steps you need to take. If you feel like you understand something, trying to distill it into simple prose often reveals a gap in understanding.

Some prompts (these are just to get you thinking; feel free to use your own):

Assignments

There will be weekly(-ish) assignments, roughly scheduled as: out on a Wednesday, due in one week. Solutions must be LaTeXed (I will post a template for you to use), submitted as a PDF via Gradescope before class on the due date. See the schedule for dates. (More details about submitting to Gradescope will be sent with the first assignment.)

These will be a mix of exercises from the textbook and a more challenging problem. Most of the grading will be binary (you make a good effort at the problem or not), and one or two problems will be graded in detail. You will (hopefully) learn something new—not covered in lecture—in the course of doing the assignment.

I encourage you to discuss assignment problems with your classmates. Solutions must be written up independently. Additionally, please state who and/or what materials you consulted while working on the assignment.

Exams

There will be a midterm and a final exam, both take-home. The midterm is tentatively scheduled for October 27. More details to be announced.

In-person class

Covid Safety in the Classroom

Masks: Masks are required for all indoor public spaces on campus, including classrooms, as per the BC Public Health Officer orders and UBC policy. For our in-person meetings in this class, it is important that all of us feel as comfortable as possible engaging in class activities while sharing an indoor space. For the purposes of this order, the term “masks” refers to medical and non-medical masks that cover our noses and mouths. Masks are a primary tool to make it harder for Covid-19 to find a new host. You will need to wear a medical or non-medical mask for the duration of our class meetings, for your own protection, and the safety and comfort of everyone else in the class. You may be asked to remove your mask briefly for an ID check for an exam, but otherwise, your mask should cover your nose and mouth. Please do not eat in class. If you need to drink water/coffee/tea/etc, please keep your mask on between sips.

Students who need to request an exemption to the indoor mask mandate must do so based on one of the grounds for exemption detailed in the PHO Order on Face Coverings (COVID-19). Such requests must be made through the Center for Accessibility (info.accessibility@ubc.ca). Mask wearing protects you as well as others in your environment. Let’s do everything we can as a community to stop the spread of this virus.

Vaccination: If you have not yet had a chance to get vaccinated against Covid-19, vaccines are available to you, free, and on campus (http://www.vch.ca/covid-19/covid-19-vaccine). The higher the rate of vaccination in our community overall, the lower the chance of spreading this virus. You are an important part of the UBC community. Please arrange to get vaccinated if you have not already done so.

Seating in class: To reduce the risk of Covid transmission, please sit in a consistent area of the classroom each day. This will minimize your contacts and will still allow for the pedagogical methods planned for this class to help your learning.

Your personal health

If you’re sick, it’s important that you stay home, no matter what you think you may be sick with (e.g., cold, flu, other). 

A daily self-health assessment is required before attending campus. Every day, before coming to class, complete the self-assessment for Covid symptoms using this tool: https://bc.thrive.health/covid19/en

Do not come to class if you have Covid symptoms, have recently tested positive for Covid, or are required to quarantine. You can check this website to find out if you should self-isolate or self-monitor: http://www.bccdc.ca/health-info/diseases-conditions/covid-19/self-isolation#Who.

Your precautions will help reduce risk and keep everyone safer.

Instructor health

I will do my best to stay well, but if I am ill, develop Covid symptoms, or test positive for Covid, then I will not come to class. If that happens, then either class will be held on Zoom or there will be a temporary replacement instructor.