Abstraction

An experimental foundation for statistics

In a recent conversation with Brian (of abstraction fame) about the relationship between mathematics and statistics. Statistics, for historical reasons, has been treated as a mathematical sub-discipline (this is the NSF’s view). One reason statistics is viewed as a sub-discipline of math is because the foundations of statistics are built on the basis of deductive reasoning, where you start with a few general propositions or foundations that you assume to be true and then systematically prove more specific results.

On the relative importance of mathematical abstraction in graduate statistical education

_Editor’s Note: This is the counterpoint in our series of posts on the value of abstraction in graduate education. See Brian’s defense of abstraction on Monday and the comments on his post, as well as the comments on our original teaser post for more. See below for a full description of the T-bone inside joke*._** Brian did a good job at defining abstraction. In a cagey debater’s move, he provided an incredibly broad definition of abstraction that includes the reason we call a a smiley face, the reason why we can apply least squares to a variety of data types, and the reason we write functions when programming.