2. Topics Covered

This lecture goes over the topics covered in the course. I don’t have much to add here, but I do have some notes about each homework and the corresponding units that might be handy.

Homework 1

Units covered: 1–3

We start out with a very brief review of probability and an introduction to Bayes’ rule. The first homework generally has questions that don’t require any calculus, just basic probability rules. They may include circuit problems, use of Bayes’ Rule, the Law of Total Probability, sensitivity and specificity, positive or negative predictive value (PPV/NPV), and simple Bayesian networks. These problems can be trickier than they seem at first!

Homework 2

Lessons covered: 4.1–4.9

We start to discuss random variables, distributions, and Bayesian inference with conjugate cases.

Homework 3

Lessons covered: 4.10–4.19

Here we get into hypothesis testing, ways to describe the posterior, different priors and their effects, and a brief discussion of Empirical Bayes methods. We’re still using conjugate cases to find posteriors.

Homework 4

Unit covered: 5

This unit we mostly move away from conjugate problems and start discussing MCMC methods for sampling from the posterior. Usually we’ll have one Metropolis-Hastings and one Gibbs sampler question.

Midterm

Units covered: 1–5

The midterm could include anything from the first half, but tends to focus on Units 4 and 5.

Homework 5

Units covered: 6–7

This is where we start using Probabilistic Programming Languages (PPLs) like BUGS, Stan, or PyMC. We start with linear regression and move into hierarchical models.

Homework 6

Units covered: 8–9

Unit 8 discusses missing and censored data along with time-to-event models. Unit 9 goes into model building, selection, and checking.

Final

Units covered: 1–10

The final is comprehensive but tends to focus on concepts from the second half of the course.

Project

There’s also an open–ended project. It could potentially be based on any part of the course, but most students opt to try out or extend the models from the second half of the course. Some of the most interesting projects I’ve seen, however, have been based on concepts from the first half, so don’t limit yourself!