Syllabus
STAT 460/560, 2026 WT1: 10 Sep. 2026 – 22 Dec. 2026
Acknowledgement
UBC’s Point Grey Campus is located on the traditional, ancestral, and unceded territory of the xʷməθkʷəyəm (Musqueam). The land it is situated on what has always been a place of learning for the Musqueam, who for millennia have passed on their culture, history, and traditions from one generation to the next on this site. We are fortunate to study, work, live, and play in this place. My sense of place here includes being aware of the fact that there are many ways of knowing and of acquiring knowledge. In this course, we get to explore some that have particularly precise and formal structures.
More information: https://indigenous.ubc.ca/
Course information
STAT_V 460: Statistical Inference I or STAT_V 560: Statistical Theory I
Winter Term 1, 2026
3 Credits, In-person only.
Prerequisite: MATH 320, STAT 305, and one of MATH 152, MATH 221, or MATH 223.
Course description
Calendar description: Statistical models and their properties, estimation methods, properties of point and interval estimation, likelihood, Bayesian inference. Intended for Undergraduate Honours or Graduate students.
Detailed description: Statistical inference (as a topic) traditionally includes two branches: estimation (or learning) of quantities of interest from data, and inference (typically focusing on hypothesis testing but more broadly construed as uncertainty quantification). It makes a formal bridge between the mathematics of probability theory and the practicalities of learning from data, often to make decisions. In this course, we will focus on how to use mathematics to formulate and state precisely what properties we can expect statistical techniques to have, and under what conditions. We will move quickly and cover a wide range of topics, getting exposure to general statistical methods (e.g., bootstrap estimation, parametric inference, model selection, simulation) and general theoretical techniques (e.g., asymptotic analyses of estimators). We will cover theory with a focus on practical implications, and may use computation as a tool for learning. At the end of the course, students should have a good knowledge of classical and modern methods for statistical estimation, including estimating uncertainty, and a strong foundation for mathematical analysis of statistical methods.
Learning methods: Learning in this course is a collaborative effort led by you, with support from the teaching team. Learning will be evaluated based on a combination of individual and group work emphasizing regular practice, resourcefulness, and engaging with the concepts in ways that are meaningful to you. (Details are in Assessments.)
Class meetings: Regular attendance and participation are an important part of your learning in the course. Class meets in person two times per week for 80 minutes (dates and times on Canvas). Please come to class having engaged with the assigned reading, completed any assigned pre-class work, and prepared to work on the in-class activities (more below).
Teaching team
Instructors: Daniel J. McDonald and Ben Bloem-Reddy
Be sure to include “STAT 460/560” in the subject line of any email to the teaching team.
- Email for Daniel:
daniel at stat dot ubc dot ca - Email for Ben:
benbr at stat dot ubc dot ca - Office hours: See Canvas
TA: TBD
- Email: See Canvas
- Office hours: See Canvas
Teaching approach
We approach this class knowing that every student enters with different preparation, and with different goals. We will do our best to support your learning, regardless of from where you’ve come or where you’re going. This course can be challenging, and we are striving to make it a collaborative endeavour in which we work together to learn with and from each other. There will be plenty of opportunities for help and advice from peers and from the teaching team. Please reach out if there is something we could do better. Suggestions, ideas, etc., are always welcome.
Commitment to equity and inclusion
We are committed to supporting an inclusive learning environment, and we are continually learning how best to do so. If you have concerns that we or someone else may not be upholding this commitment, we invite you to either talk with us if you feel comfortable, or share your thoughts with the department. If in class discussions there are derogatory, harassing or hateful statements made, we will intervene to help prevent further harm and uphold a respectful class environment. Our pronouns are he/him/his, and we invite you to use the option on Canvas to provide your pronouns (find out how in the Canvas Student Guide).
Course objectives
If you are willing and able to meet the requirements, by the end of this course you will be able to:
- understand technical statistical language and ideas in research papers, when explicitly stated and otherwise (the latter situation is especially common outside of statistics journals);
- define and manipulate the estimation and uncertainty quantification aspects of a statistics or machine learning problem;
- define and analyze statistically meaningful theoretical properties of core statistical methods;
- understand the process of constructing a mathematical analysis of a statistical procedure;
- communicate your thinking about statistical analysis verbally and mathematically;
- learn related and advanced topics through self-study.
Learning materials
Textbooks
All of the required textbooks are available as PDFs through the UBC library. You can also purchase a hard copy if you prefer.
Primary textbooks:
L. Wasserman, All of Statistics. Primary text for first half of the course. [AoS]
A. van der Vaart, Asymptotic Statistics. Primary text for the second half of the course. [vdV]
Complements and references:
L. Wasserman, All of Nonparametric Statistics. [AoNS]
B. Efron and T. Hastie, Computer Age Statistical Inference. [CASI]
M. Schervish, Theory of Statistics.
M. Wainwright, High-dimensional Statistics: A Non-asymptotic Viewpoint.
J. Jacod and P. Protter, Probability Essentials.
M. A. Proschan and P. A. Shaw, Essentials of Probability Theory for Statisticians.
Class sheets
Additional lecture notes with examples and exercises will be posted to Class sheets. These are intended to complement the textbooks and will be discussed in class. They are not intended to be a complete set of notes for the course, and you are responsible for the material in the textbooks.
Communication
We will use Canvas to make announcements.
Please use email for course-related communications (or talk to us before/after class).
Course structure and learning activities
It is imperative that you read the assigned sections of the textbook(s) prior to class and complete any assigned pre-class work. I will cover only certain topics in detail; much of the class time will be devoted to individual and group learning activities that depend on you reading before class.
Course schedule
The course schedule is available at Course schedule. The schedule is subject to change, and will be updated as necessary. Please check the schedule regularly. Important changes will be announced in class and on Canvas.
Assessments of learning
Your final grade will be calculated as follows:
| Category | Contribution | Notes |
|---|---|---|
| Pre/In-class assignments | 10% | See description below |
| Assignments | 20% | (roughly) every week; see description below |
| Midterm exam | 35% | Scheduled for October 20; more details to follow |
| Final exam | 35% | Exam period is December 11–22; more details to follow (UBC typically confirms dates in mid-October) |
Your average between the midterm and final exams must be at least 50% in order to pass the course.
My primary concern is that you learn mathematical statistical estimation/inference to the level of the course objectives. If you work hard and demonstrate what you are learning (via assignments, in-class participation, office hours attendance, etc.), you will do fine.
Pre/In-class assignments
As an incentive to keep up with the reading and come to class prepared, most Tuesday classes will have a small amount of assigned work. This work is to be either completed on Canvas, or done during the first 5 to 10 minutes of class. The work is not intended to be overly difficult or time-consuming.
Participation
Each class meeting we will involve a number of activities, typically structured as “think-pair-share”: I describe a problem, everyone thinks/works independently for a few minutes, we discuss our thoughts/work in pairs or small groups, and then someone volunteers to share with the entire class. The point is not necessarily to get the exercise correct; it is to practice thinking through a problem and communicating your thinking. Engaging in each step of the activity is important for your learning.
Assignments
There will be assignments, roughly weekly. Solutions must be LaTeXed (template on the Assignments page), submitted as a PDF via Canvas before class on the due date.
These will be a mix of exercises from the textbook and more challenging problems. 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. Learning in this class is a team sport! Solutions must be written up independently. Additionally, please state who and/or what materials you consulted while working on the assignment; feedback is optional and welcome.
Exams
There will be a midterm exam on October 20, and a final exam sometime during the December exam period (to be scheduled by UBC). More information on format and topics covered will be given closer to the exam dates.
Policy statements
Academic integrity
From the UBC website on academic integrity:
Doing your own work, acknowledging the contributions of others, and seeking help when you need it are all part of what academic integrity means at UBC, as is avoiding tools and services that subvert these practices.
Academic integrity is a commitment to upholding the values of respect, integrity, and accountability in academic work. It is foundational to teaching and learning and is a fundamental and shared value of all members of the UBC community. UBC adopts an educative approach to academic integrity that supports students and instructors around awareness and that values academic misconduct processes that are fair and effective.
Academic integrity is a set of values and skills that must be learned and refined over time. Instructors are responsible for setting clear expectations around academic integrity in their courses, modelling honest behaviour as teachers and scholars, and creating a space for students to develop their understanding of academic integrity. Students are responsible for meeting these expectations in their academic work, developing an understanding of concepts, and seeking support when they have questions. UBC is responsible for creating and sustaining the culture of academic integrity that makes all of this possible.
Everyone plays a part in supporting and enhancing academic integrity at UBC.
In this course, you are expected to do your own work on out-of-class assignments (see assignments). Any people or resources consulted while working on your assignments must be acknowledged on the work you submit.
Use of generative AI
Using generative AI tools such as (but not limited to) ChatGPT or Claude is allowed only for searching for information in the same way as you use a search engine. The following uses are strictly prohibited and would be considered academic misconduct.
- Obtaining full or partial solutions to assigned problems.
- Generating computer code or figures for your assignments.
- Using generative AI to summarize course materials, including lecture notes, textbooks, or other resources.
- Using generative AI to prepare Exercises or Activities in advance of class.
Many of the above uses are not only prohibited, but also counterproductive to your learning. You will not learn the material if you use generative AI to do your work for you. If you are unsure about whether a particular use of generative AI is allowed, please ask the instructor.
Many authoring tools (including Overleaf, Microsoft Word, VSCode, and Google Docs) have built-in generative AI features. You may NOT use these tools for writing your assignments. You should be careful to turn off any generative AI features in your authoring tools before you start writing your assignments.
This list is not exhaustive.
If you are unsure, ask the instructor.
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 assault. 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, spiritual 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 on the UBC Senate website.
Additional course policies
Health and in-person class
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).
If you do miss class because of illness:
- Let me know as soon as possible.
- Make a connection early in the term to another student or a group of students in the class. You can help each other by sharing notes.
- Do your best to keep up with the reading, exercises, and assignments. The “late day” policy for assignments is intended to help with such situations, and can be adapted as needed.
Instructor health
I will do my best to stay well, but if I am ill then I may not come to class. If that happens, then either class will be held on Zoom or there may be a temporary replacement instructor. Our classroom will still be available for you to sit and attend an online session, in this (hopefully rare) instance.
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.
Assignments
The default policy for assignments is that you have three “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 0.8 each day that it is late. If you are using a late day, you must let the TA know before the assignment is due. See Canvas for their contact information. If you have extenuating circumstances, please contact me as soon as possible.
Exams
Both the midterm and final exams are treated equally in terms of importance. It is very important that you attend both exams. Missing the midterm exam is handled by the teaching team. In-term concessions for the midterm exam will be granted only in exceptional circumstances. Missing the final exam is handled by your Faculty Advising Office.