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GAINING WEIGHT... posted:I'm not sure about this. I think throwing in order of birth is just a red herring. B G and G B are the same "possibility" for Bill; each family can either have two girls or one of each. Fifty fifty. No, he's absolutely right about 67%. Trust me when I say statistics are often incredibly unintuitive- but you really need to take a course on Bayesian inference to understand the key difference between Bob and Bill. Prior information is key- which is why this is superficially similar to Monty Hall. Other weirdly unintuitive applications of Bayes theorem reveals: -Getting a positive result on a mammogram only results in a 20% chance of actually having cancer (as it is much more likely to be a false positive when the population rate is taken into account) -DNA evidence is questionable without prior suspicion; given only DNA evidence tying someone to a crime, is far more probable that person belongs to the population of false positives than true positives. -by extension, this is also why blanket testing policies for whole populations (testing everyone for allergies; screening welfare recipients for drug use) is garbage- specificity of tests are never perfect, and without the benefit of prior knowledge (suspicion of allergy in first case, drug use in the latter) you'll have more false positives than true. A Buttery Pastry posted:
It's still true, and the posterior probability of a BG pair is still higher, it's just not as exact or as clean mathematically when you move away from 50/50.
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Sep 4, 2016 00:41
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It's not really a trick of language though. The big key to Monty Hall is he will never, under any circumstance, open the door with the car behind it. Since we know the prior chances (1 car, 2 goats), there are just two possibilities. If you pick a car, he picks a goat randomly; If you pick a goat, he reveals the other goat. This data must be considered: Switching from a goat door to another goat door is not one of the possible outcomes of the second choice. Only switching from car to goat or from goat to car. This data has an interesting consequence: Choosing to switch is essentially betting on the chance that you picked wrong on the first choice. That happens to be 66%. PoizenJam fucked around with this message at 03:55 on Sep 4, 2016 |
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Sep 4, 2016 03:51
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I dunno- statistical inference is pretty unintuitive, and at least has the appearance of looking paradoxical. If we were only discussing true paradoxes... Well, they're wouldn't be much to discuss. They're unsolvable by definition.
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Sep 4, 2016 16:29
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Well, if this thread has taught me anything, it's that a bayesian statistics unit/chapter would be a huge boon to high school curricula.
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Sep 7, 2016 18:21
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