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I'm probably missing something, but Baye's Theorem seems quite overrated in this corner of the internet. (I've read all of the Sequences + the Arbital Guide)
You have an idea of how likely something is to happen, or an estimate of a figure, or a model of something in the real world (e.g: Peter is a guy who loves cats). You happen to get new information about this something (e.g: you see Peter viciously killing a cute kitten).
You'd most likely update, with both epistemical consequences (you'd probably stop believing Peter is the cat-loving guy you thought) and instrumental or practical consequences (you wouldn't ask him to look after your cats while you are away on holiday).
The way I see it, Bayes' Theorem tel... (read more)