Bayesian updating definition

So let me try to offer my definition, which boils Bayesianism down to three core tenets.

A brain tumor always causes a headache, but exceedingly few people have a brain tumor.

In contrast, a headache is rarely a symptom for cold, but most people manage to catch a cold every single year.

Given no other information, do you think it more likely that the headache is caused by a tumor, or by a cold?

This article is an attempt to summarize basic material, and thus probably won't have anything new for the hard core posting crowd.

It'd be interesting to know whether you think there's anything essential I missed, though.

You've probably seen the word 'Bayesian' used a lot on this site, but may be a bit uncertain of what exactly we mean by that.You may have read the intuitive explanation, but that only seems to explain a certain math formula.There's a wiki entry about "Bayesian", but that doesn't help much.And the LW usage seems different from just the "Bayesian and frequentist statistics" thing, too.As far as I can tell, there's no article explicitly defining what's meant by Bayesianism.The core ideas are sprinkled across a large amount of posts, 'Bayesian' has its own tag, but there's not a single post that explicitly comes out to make the connections and say "this is Bayesianism".