I don’t get the sock drawer problem. Intuitively it’s as described. But say I’m blind. Then every 10% per drawer divides into like 1% per square inch in my drawer (I have to feel my way through the whole drawer). Remembering “80% that I put it in one of these drawers” should have that probability waterfall running down, amassing in the last drawer. Otherwise if the sock is in the last drawer’s furthest corner - my odds would be 1:20 for feeling through the whole room / house instead of exhausting the 80% I’ve allocated to my “drawer area”. Sure, I’d be mighty anxious when I’m down to the last drawer. But still. Can anyone point out my mistake? Thanks!
From earlier pages, this will be harder than it initially appears.
Say that, on hearing there was a dagger, the king also ponders what other things an assassin might carry. Poisons, for sure - an assassin would have them like 6:1 odds at least, and a non-assassin would be surely no more than 0.02:1.
Listening devices, for spying and stuff. Probably 4:1 and 0.02:1 again.
Naive Bayesian analysis would say that doctors, with their knives and stethoscopes and drugs, would be carrying tools with odds of 9 * 6 * 4 : 1 = 216 : 1 if they were an assassin, and 0.02 * 0.02 * 0.3 = 0.00012 : 1 if they were not.
It's very easy to forget that "updated odds" are also "updated conditions". The king has not updated his odds of that person being an assassin; they have replaced their odds of "the person" being an assassin, with some new odds of "the person with the knife" being an assassin.
Subsequent odds need to be added in that light. The need to accurately track the decreasing weight of subsequent pieces of evidence feels like it is unlikely to be intuitively grasped by most.
I'm not clear on why we wouldn't revise this estimate of the probability that we didn't put our socks in the dresser?
I don’t get the sock drawer problem. Intuitively it’s as described. But say I’m blind. Then every 10% per drawer divides into like 1% per square inch in my drawer (I have to feel my way through the whole drawer). Remembering “80% that I put it in one of these drawers” should have that probability waterfall running down, amassing in the last drawer. Otherwise if the sock is in the last drawer’s furthest corner - my odds would be 1:20 for feeling through the whole room / house instead of exhausting the 80% I’ve allocated to my “drawer area”. Sure, I’d be mighty anxious when I’m down to the last drawer. But still. Can anyone point out my mistake? Thanks!
From earlier pages, this will be harder than it initially appears.
Say that, on hearing there was a dagger, the king also ponders what other things an assassin might carry. Poisons, for sure - an assassin would have them like 6:1 odds at least, and a non-assassin would be surely no more than 0.02:1.
Listening devices, for spying and stuff. Probably 4:1 and 0.02:1 again.
Naive Bayesian analysis would say that doctors, with their knives and stethoscopes and drugs, would be carrying tools with odds of 9 * 6 * 4 : 1 = 216 : 1 if they were an assassin, and 0.02 * 0.02 * 0.3 = 0.00012 : 1 if they were not.
It's very easy to forget that "updated odds" are also "updated conditions". The king has not updated his odds of that person being an assassin; they have replaced their odds of "the person" being an assassin, with some new odds of "the person with the knife" being an assassin.
Subsequent odds need to be added in that light. The need to accurately track the decreasing weight of subsequent pieces of evidence feels like it is unlikely to be intuitively grasped by most.