Syllabus: STAT405 Bayesian Statistics

Course description

Bayesian inference is a flexible and powerful approach to modeling reality, making optimal predictions from data, and quantifying uncertainty in a coherent manner. Thanks to their versatility, Bayesian methods are now widely used in virtually all fields of science, engineering, and beyond.

In STAT 405, you will:

  • design probabilistic models to approach real-world inferential problems;
  • perform inference using Bayesian modelling languages;
  • critically assess, debug, and iteratively improve Bayesian workflows;
  • develop and analyze custom posterior approximation machinery.

Note: this course was called 447C in previous years.

Lecture time and place

Lecture dates: Tuesday and Thursday, 9:30-11:00. See Canvas for location. Detailed schedule

Teaching team

Prerequisite

  • Probability: One of MATH 302, STAT 302, or MATH 418
  • Inference: either STAT 305 or STAT 460
  • Computing: we will use R in the homework and during lectures. If you know another programming language but not R, you can still take this course but be prepared to spend a bit of extra time to get familiar with the R syntax. We will have special office hours sessions at the beginning of the term to help you doing that.

Come talk to me at the end of the first lecture if you are unsure about your preparation for this course.

Software

All software used is free and open source. Some key tools we will use:

We assume you have a laptop on which you can install these tools, if not, you may be able to borrow one from UBC library.

Textbook

Notes will be provided and complemented with readings from the following freely available textbook:

  • Bayesian Data Analysis, Third Edition. Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin. PDF freely available.

Additional readings and case studies will be drawn from other textbooks that are either freely available or available within UBC VPN:

Assessments

Click on each item for details.

  • Participation: 7%. Each week, do at least one of:
    • Weekly reading assignment: ask one thoughtful question, or participate meaningfully in an answer/discussion thread about the readings on Piazza, or,
    • go to a lab or office hour on that week and fill the sign up sheet, or,
    • if you really do not have any question, post a comment, e.g., website you found useful to learn the material.
  • Low-stake questions: 8%. In-class iClicker questions: binary participation points (attempted vs not), unless your score is indistinguishable from random.1 Setup iClicker Cloud on Canvas. See also challenge questions below.
  • Homework exercises: 15%
    • Weekly (look for the ‘Exercises’ page for the corresponding week on this website).
    • Submit on Canvas.
  • Quizzes (2 x 20%): 40%
    • In-class, closed-book.
    • Dates: February 24 and March 24
  • Final project: 30%

For the participation and homework, we will drop the lowest week. For the iClicker, we will automatically skip up to two missed lectures. Do not ask for additional accommodations, this is the accommodation, i.e., keep these for sick days/unforeseen circumstances. On the positive side, no need to ask for permission/provide doctor’s note, this will be done automatically for everyone.

For exercise grading, I will take the \(\max(\text{mean}(e_1, e_2, ...), \text{mean}(e_2, e_3, ...)), \text{mean}(e_3, e_4, ...))\), where \(e_1, e_2, e_3, \dots\) are the scores for the different exercises. The same applies for clicker participation points. This is in place to help a couple students travelling in the first two weeks, but will be automatically applied for everyone so no need to request it.

Once in a while, I will post some challenge questions. These are not essential for learning the material and can be skipped. Submit your answer at any time. For each that you successfully solve, a week of iClicker participation will be waived (it does not have to be the same week you submit the challenge question). I will not post solutions for the challenge questions.

Policy on the use of AI tools

  • Piazza discussion: use of AI tools is prohibited to compose or answer questions, with the exception of spell-checking tools.
  • Homework: use of AI tools is prohibited, with the exception of spell-checking tools.
  • Quizzes: use of AI tools is impossible (closed book, pen and paper).
  • Project: if you think AI tool(s) will be used, explain the scope of their use in the project proposal. Also describe all uses in the final report.

Office hours

Friday, 1pm, ESB 3125.

Available by appointment if you are unable to attend drop-in hours.

Course communication

Announcements

Course announcements will be posted on Canvas.

Questions

Use Piazza for questions about the material, logistics, etc. Use public posts as much as possible so that other students can learn from the discussion.

Use canvas messages if, and only if the question is about a personal matter.

Footnotes

  1. How is it possible to determine if a score is indistinguishable from random? This is exactly the kind of problem you will be able to solve after taking this course. We will cover a Bayesian hierarchical model that can do that in week 10 of this course.↩︎