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DanielVarga comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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Wonderful. Are you aware of the Tuesday Boy problem? I think it could have been a more impressive second example.
(The intended interpretation is that I have two children, and at least one of them is a boy-born-on-a-Tuesday.)
I found it here: Magic numbers: A meeting of mathemagical tricksters
Actually, a Bayesian and a frequentist can have different answers to this problem. It resides on what distribution you are using to decide to tell me that a boy is born on Tuesday. The standard answer ignores this issue.
I don't know much about the philosophy of statistical inference. But I am dead sure that if the Bayesian and the frequentist really do ask the same question, then they will get the same answer. There is a nice spoiler post where the possible interpretations of the puzzle are clearly spelled out. Do you suggest that some of these interpretations are preferred by either a frequentist or a Bayesian?
Well, essentially, focusing on that coin flip is a very Bayesian thing to do. A frequentist approach to this problem won't imagine the prior coin flip often. See Eliezer's post about this here. I agree however that a careful frequentist should get the same results as a Bayesian if they are careful in this situation. What results one gets depends in part on what exactly one means by a frequentist here.