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ruidh
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I don't know anything about the credence stuff, but I do know probability. Bayes' Theorem is useful here. I don't like their notation. I think it causes confusion. I'm going to use H:Heads, Ta:Tails, M:Monday, Tu:Tuesday. So, their T1 v T2 is just Ta. T1 v H1 is M. We are interested in Pr(H|M) -- our posterior estimate of Pr(Heads) given that we're told it's Monday. Mr Bayes tells us Pr(H|M) = Pr(M|H)*P(H)/Pr(M). But Pr(M|H) = 1. So Pr(H|M) = P(H)/Pr(M) Lets look at Pr(M). Pr(M) = 1-Pr(Tu) Pr(Tu)=Pr(Tu|Ta)*Pr(Ta)/Pr(Ta|Tu). But Pr(Ta|Tu)=1, so Pr(Tu)=Pr(Tu|Ta)*Pr(Ta) What is Pr(Tu|Ta)? I can argue that it is 1/3. She gets woken twice on Monday and once on Tuesday. If she has just been woken and doesn't know the day, it's twice as likely that it's Monday than Tuesday if the coin was Tails. Pr(Tu)=1/3*Pr(Ta) If Pr(Ta)= 1/2 (i.e. a fair coin), so Pr(Tu)=1/6 And Pr(M)=5/6 Another way to look at it is half the time you get woken up twice on Monday and the other half the time you get woken up twice on Monday and once on Tuesday Pr(M) = 1/2*1 + 1/2*(2/3) = 5/6 Back to Pr(H|M) = P(H)/Pr(M) Pr(H|M) = (1/2)/(5/6) = 3/5 3/5. Not 2/3. Not 1/2. Your posterior estimate of the likelihood of heads is higher. This bothers people because the coin hasn't been thrown yet. But what if it had been thrown on Sunday and the result hidden to everyone until the time of the second waking? We can talk about the likelihood of that actual coin throw which has occurred. Delaying the throw form Sunday to Monday doesn't change our estimate. But what is I think Pr(Tu|Ta) is 1/2? I think this is wrong, but it leads to Pr(Tu) = 1/4 and Pr(M) = 3/4 Here Pr(H|M) is Pr(H|M)=(1/2)/(3/4) = 2/3 So, I think there is some fuzziness in the presentation of these two gentlemen. A simplistic view could support the idea that Pr(Tu|Ta) is 1/2 -- It's either Monday or Tuesday, isn't it? Two possibilities. but not two equally likely possibilities. This is still counter-intuitive stuff and it's the kind of stuff that makes people tear their hair out at Bayes.
There's nothing new about privacy and oversharing. I've been on email lists for over a decade and the advice then still holds -- don't post anything you wouldn't mind being taked up on the breakroom wall where you work. Facebook is, at least, an advance over email lists as you have the tools to control where your posts go. You can restrict your posts to friends or friends of friends or even to a small group that might appreciate a quirky joke. II've live art of my life online for a while now and I find Facebook is one of the better resources.