A.2 Course objectives: what is this course for?

A.2.1 The big picture

If it helps, here’s how I think about the core MHC Stat curriculum: * Stat 140: what? * Stat 242: how? * Stat 343: why? * …and Stat 340: what else?

This course is called “Mathematical Statistics,” which is…correct but vague. You may find it helpful to think of it as “the more-theory upper-level core course.” So why do you need all this theory? As I see it, there are three main reasons:

  • You need to understand why a method works in order to really know how to use it. When will it break? Why will it break? When and why might something else be better? As a statistician, your job is not to say “ok i ran a \(t\) test byeeeeeee” – you need to know why you’re doing what you’re doing.
  • You need to understand theory in order to develop and assess new methods.
    • This isn’t just for folks going on to a PhD in Statistics! Even working in a “regular job,” you may need to develop or adapt methods in order to solve a specific problem. I get a lot of my methodology-research projects from industry collaborators.
  • Math is cool and beautiful <3

You may feel more connection to one or the other of these reasons – or to some other reason entirely – and that’s fine :)

So we’re going to spend a lot of time asking “why?” Sometimes we’ll ask “why is this statement true?”, as in a conventional math proof. But sometimes we’ll ask things like “why does this proof work?” or “why is this condition/restriction/definition important?” or “why does this result matter in terms of this other thing?” Digging into these whys, and communicating both the questions and the answers, are the two big skills you’ll work on in the course.

A.2.2 Specific objectives

The key statistical concepts we’ll work with in this course are divided into 18 learning goals. These goals are batched together into 6 modules. You can see the list below; you’ll get more details about what each one involves as we get closer to it.

You’ll build your communication skills by interacting with your classmates (and me!) throughout the semester, both formally and informally, and with a small project presentation.

Modules:

  1. Probability
  2. Parameter estimation (focused on theory and classical methods)
  3. Bayesian methods (still talking about parameters though!)
  4. Estimator behavior (including large-sample results)
  5. Interval estimation
  6. Hypothesis testing

Let me take this moment, though, to remind you that I’m neither omniscient nor omnipotent. Things might change :)