Justin B. Post

Math Stat Blog Purpose & Rationale

In most graduate (and undergraduate) statistics programs two courses on probability and statistics form the core theory courses. Historically, the courses were taught solely using pen and paper where:

the first course focused on probability theory and properties of random variables
the second course looked at finding estimators and their properties, forming confidence intervals, and deriving hypothesis tests

While I don’t think there is anything inherently wrong with the traditional setup for the courses, there are a few issues that often pop up:

intuition about the theory often gets lost in the details
the mathematics and calculus used in derivations obscures the concepts
linking theory and practice can be difficult for those just entering the statistics discipline

At NC State we decided to split our first year PhD theory courses from our master’s level theory courses. I had the opportunity to design these new master’s level courses! With this fantastic opportunity I tried to modernize the treatment of the theory courses. While the core theory is still covered, I put an emphasis on:

the infusion of computing (via R) to simulate data for exploration of concepts and gaining intuition about results
provide a dedicated focus on the ‘why’ of the material linking the ideas to statistical inference in the first course rather than waiting until the second course
utilizing Monte Carlo simulation studies to look at large-sample theory and the performance of competing confidence interval and hypothesis testing methods
introducing modern ideas such as the bootstrap and MCMC sampling

The courses have been very well received. The main difficulty in transitioning the course to the format is finding an appropriate book to use that students can read and understand (and of course you can pull problems from!). For years I’ve used the book by John Rice - Mathematical Statistics and Data Analysis. The book is very solid but doesn’t exactly go in the order used in my course and, of course, the changes to the traditional sequence aren’t all there.

As such, I’ve created a lot of notes, examples, and activities myself. The purpose of this blog is to share those examples and discuss the teaching of these types of courses! There was an excellent session at JSM 2022 about the modernization of the mathematical statistics sequence (in many of the same ways I’m discussing here).

List of posts:

Coming soon