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The SE answer looks like it assumes that blue cars aren't "stupidly rare", but I don't see that reflected in any of the math. Is there a word for that assumpti
by jancsika 9y ago
The SE answer looks like it assumes that blue cars aren't "stupidly rare", but I don't see that reflected in any of the math.
Is there a word for that assumption in statistics? I'm guessing this is something that is so obvious to a statistician that they don't even think to include it. But without seeing the work the layperson is likely to throw up their arms and say, "Not enough information."
- jonahx 9y agoThe assumption is worked in. He assumes a base rate of only 0.1% of all cars are blue, and then shows that even with this it is astronomically unlikely the car isn't blue. He could have explicitly calculated how low a base rate you'd need for, say, a 50% chance the car is blue, and that number would be astronomically small as well. While working the numbers was needed for the SE answer, I actually think it obscures the intuition. The high order bit here is that there's only a 10% chance of a false positive, and so you're raising 0.1 to the 900th power. Everything else is a second order term relative to that, and you can instantly see the answer will be "nearly certain".
- yorwba 9y agoThe answer calculates a likelihood ratio of 10^763, so for a 50% chance you'd need a prior probability of less than 1/(10^763 - 1) ≈ 10^(-763), which would imply that there is most likely not a single blue car in the universe.
- GlennS 9y agoNot a statistician, but I think you'd call it a 'prior'. https://en.wikipedia.org/wiki/Prior_probability https://en.wikipedia.org/wiki/Prior_probability