My Bayesian Enlightenment — LessWrong
I remember (dimly, as human memories go) the first time I self-identified as a "Bayesian". Someone had just asked a malformed version of an old probability puzzle, saying: If I meet a mathematician on the street, and she says, "I have two children, and at least one of them is a boy," what is the probability that they are both boys? In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys. But in the malformed version of the story—as I pointed out—one would common-sensically reason: If the mathematician has one boy and one girl, then my prior probability for her saying 'at least one of them is a boy' is 1/2 and my prior probability for her saying 'at least one of them is a girl' is 1/2. There's no reason to believe, a priori, that the mathematician will only mention a girl if there is no possible alternative. So I pointed this out, and worked th