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If that student flipped 200 heads in a row it isn't survivorship bias. That student has a two headed coin.
by yters 9y ago
If that student flipped 200 heads in a row it isn't survivorship bias. That student has a two headed coin.
- zeefoo 9y agoIt most certainly can be. 200 heads in a row is entirely possible in a random run.
- yters 9y agoIf you think 200 heads in a row is practically possible on a random flip, I have a bet to make with you.
- seanmcdirmid 9y agoFlipping heads 200 Times is definitely possible, I can do the math to prove that. It is just greatly improbable to happen in the space or lifetime of the universe.
- yters 9y agoProbabilities can be so small they are only possible in a mathematical sense, but impossible practically speaking. When faced with such small probabilities we can use Bayes theorem to infer a better explanation than chance, such as a two headed coin.
- the_cat_kittles 9y agolol @ u spouting nonsense. i think your trying to say you can use bayes to adjust for small sample sizes, like with beta-binomial models, or comparing posterior distributions for different models and params.
- yters 9y agoTwo sequences of coin flips: HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH THTHTHHTHTHHHHHHHTTTHTHHHTHHTT Which was generated by fair coin, which by 2 headed? How did you decide?
- seanmcdirmid 9y agoHHH.... is possible from a head fail fair coin, just improbable. If it happened, I would be astounded, but I wouldn’t feel like logic or the laws of the universe were being violated (I would look for a reality reset button though to pick out the improbable but not impossible occurrence).
- the_cat_kittles 9y agoassuming you want a bayesian approach? take a flat prior and look at the MAP? though you know its just going to be the observed rate. if you know you only have a fair coin or a double head coin just compare their likelihoods? what is the point you are trying to get at?
- yters 9y agoSolomonoff induction and universal probability.
- the_cat_kittles 9y agohow about something specific. how would you answer the question you proposed used bayesian methods?
- yters 9y agoP(all heads|double headed coin) = 1 P(all heads|fair coin) = 2^{-L} Applying Bayes gets P(double headed coin|all heads) >> P(fair coin|all heads) for a long enough sequence.
- the_cat_kittles 9y agothats what i suggested originally, essentially
- kinkrtyavimoodh 9y agoEven if the class had 200 students the winner didn't need to flip 200 in a row. On average, half the students of the class would get Heads in each iteration, which means that this experiment would go on only for lg(200) iterations, which is only 7. Flipping 7 Heads in a row is not all that difficult to imagine.
- yters 9y agoMy point is large enough amounts of success cannot be attributed to survivorship bias.