In the last episode, we introduced two thinking errors that often come up in statistics: Bayes’ paradox and regression to the mean. I proposed that these errors are really two different manifestations of the same underlying phenomenon, but I haven’t done much to actually explain why. This post will lay the mathematical groundwork for that explanation!
In my intro psych class, we discussed two distinct fallacies: common systematic errors in how humans think. These are called Bayes’ Paradox and regression to the mean. I will claim that both of these are really manifestations of the same underlying issue, and in actuality are mathematically the same.
This is going to be pretty involved and pretty long, so I’ll be splitting it up into parts. The first part will just cover the basics of what these two fallacies are and provide a mathematical framework. After that I’ll be using computers to analyze the two, and then I’ll make the math behind what we’re doing more rigorous.
This is the first public page for this blog: a place where I will record thoughts and essays on various topics, usually pretty close to the intersection of math, data, and computing. There will be some pretty heavy mathematical topics as well as much lighter fare: my hope is that people of varied math and computer science backgrounds can find something useful for them.
So, hello world!1 I thought the first thing I should probably do is explain why I go by the tag
PollardsRho in various places and why I decided to give this blog the title “Pollard’s Rho.” Simply
put, it’s my favorite algorithm: kind of an esoteric category to have a favorite in, but I’m sure by
the end of this you’ll see what I mean.