It’s a generalisation of logic1.
The problem is, I have never had any formal training in it. Not even in high school. So that leaves me in a bit of a limbo because I see understanding probability as one of the cornerstones of Good Thinking.
This is my attempt at curing that.
What I shall do is start from the axioms then prove theorems as I tackle classic problems. Which means three things: a) this page will be a work-in-progress indefinitely2, b) the vocabulary I will build here may not correspond to the standard one, and c) I’ll probably get things wrong a lot of times so this may not be the best page to cite in support of your Internet argument.
Eventually, those external links should become internal ones.
These are the basic building blocks of probability theory.
Using these we can already say a few basic facts about probabilities.
What are these definitions for?
We defined the reduced universe as such because we want to be able to say, “In the universe where data set A is true…”.
What do we mean by a data set being true in the first place? Say . Then in a particular universe, is true if Alice is a mouse and if she is big and not otherwise. The truthiness of is the truthiness of all its conditions.
In this vein, saying that two data sets are independent is saying that whether or not B is true does not affect whether or not A is true: .