everything about statistics seems so sus - like law of large numbers, wtf? who's making that happen?
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it helped a lot for me to learn about large deviations inequalities. you can pretty precisely quantify how unlikely it is for a large number of iid samples from a distribution to deviate significantly from the original distribution. it’s wacky stuff
this is the gateway drug but later you’ll want sanov’s theorem
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Statistics is great for General behaviors but almost never works for predicting individual behaviors
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Part of the reason for that is by the time. You're looking at a individual they're almost by definition a outlier
for sure. it sounds like an innocent assumption but it's really not. actually quite hard to give a satisfying account of like, why we expect coin tosses or dice rolls to be even approximately iid
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But this is what people find suspicious. If you agree with the math, then Hume was wrong about induction, and we have a reason to think the future will probably be like the past, even without knowing of any "necessary connections" that would make that happen.