ChrisHibbert comments on Beautiful Probability - Less Wrong

34 Post author: Eliezer_Yudkowsky 14 January 2008 07:19AM

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Comment author: ChrisHibbert 27 July 2009 06:38:10AM 3 points [-]

"Two medical researchers use the same treatment independently [...] one had decided beforehand [...] he would stop after treating N=100 patients, [...]. The other [...] decided he would not stop until he had data indicating a rate of cures definitely greater than 60%, [...]. But in fact, both stopped with exactly the same data: n = 100 [patients], r = 70 [cures]. Should we then draw different conclusions from their experiments?"

[...]

If Nature is one way, the likelihood of the data coming out the way we have seen will be one thing. If Nature is another way, the likelihood of the data coming out that way will be something else. But the likelihood of a given state of Nature producing the data we have seen, has nothing to do with the researcher's private intentions. [...]

The expectations and the stopping rule make a difference. The reason the Monty Hall Puzzle turns out the way it does is that part of the setup is that Monty Hall always opens a different door than you chose. When I tell the story without mentioning that fact, you should get a different answer.