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Given that terrorists are very rare then the P(A|B) using your terminology (where A = terrorist and B= bad record) will be very low. But for for a fixed P(A) a

by barking 14y ago

Given that terrorists are very rare then the P(A|B) using your terminology (where A = terrorist and B= bad record) will be very low. But for for a fixed P(A) and P(B) then the higher the value there is for P(B|A) the higher the value of P(A|B) will be. If you have an enornmous haystack to search it's more efficient to look first where you're most likely to find needles.

jlgreco 14y ago
P(B|A) can be 100%, but if P(A) is astronomically small (and it is) and if P(B) very high (and it is), then P(A|B) will be so low that it becomes clear P(B|A) is absolutely worthless. As an extreme example demsonstrating the necessity of considering P(A|B), suppose we observe that 100% the 9/11 hijackers had black hair (P(black hair|terrorist) = 100%). That observation is worthless because P(terrorist|black hair) is stupidly low. Just because we can say something about the traits a terrorist will likely have does not mean that we can rationally use those traits to detect terrorists. If you are proposing a P(B|A), it is on you to show that the P(A|B) is sensible. Just pointing at a high P(B|A) alone is worthless. That's how you make good "Tonight at 11', is [common household objects] killing you slowly?!?" headlines, but that is about it.
- barking 14y ago
  In your extreme example you can see that people in the B' group (those who don't have black hair) can be safely excluded as suspects. So even in this artificial example you can see that knowing P(B|A) is of value.
  - jlgreco 14y ago
    You seem to have missed the part where the extreme example is not real life. If you exclude people without black hair from suspicion, then the baddies will find someone without black hair. You cannot assume P(B|A) will not be modified by the policies you adopt. ...well, you can if you are the TSA and don't actually have to answer to anybody.... P(B|A) will never be 100% anyway though, so even if the terrorists were unable to adapt it would not matter. The point is that even in the absurd event that you found a P(B|A) that was 100%, it doesn't mean it is useful. Or do you actually think that screening for black hair in the example would be worthwhile?
    - barking 14y ago
      You seem to have missed the part where the extreme example is not real life Actually, I referred to your example as both 'extreme' and 'artificial' in my previous post. Since the example was constructed to make your point as obvious as possible I was just pointing out that in fact P(B|A) was actually useful even in that example. Sorry for the delay in responding, I gave up yesterday because there was no option to reply even after a very long time.

by barking 14y ago

jlgreco 14y ago

P(B|A) can be 100%, but if P(A) is astronomically small (and it is) and if P(B) very high (and it is), then P(A|B) will be so low that it becomes clear P(B|A) is absolutely worthless. As an extreme example demsonstrating the necessity of considering P(A|B), suppose we observe that 100% the 9/11 hijackers had black hair (P(black hair|terrorist) = 100%). That observation is worthless because P(terrorist|black hair) is stupidly low. Just because we can say something about the traits a terrorist will likely have does not mean that we can rationally use those traits to detect terrorists. If you are proposing a P(B|A), it is on you to show that the P(A|B) is sensible. Just pointing at a high P(B|A) alone is worthless. That's how you make good "Tonight at 11', is [common household objects] killing you slowly?!?" headlines, but that is about it.

barking 14y ago
In your extreme example you can see that people in the B' group (those who don't have black hair) can be safely excluded as suspects. So even in this artificial example you can see that knowing P(B|A) is of value.
- jlgreco 14y ago
  You seem to have missed the part where the extreme example is not real life. If you exclude people without black hair from suspicion, then the baddies will find someone without black hair. You cannot assume P(B|A) will not be modified by the policies you adopt. ...well, you can if you are the TSA and don't actually have to answer to anybody.... P(B|A) will never be 100% anyway though, so even if the terrorists were unable to adapt it would not matter. The point is that even in the absurd event that you found a P(B|A) that was 100%, it doesn't mean it is useful. Or do you actually think that screening for black hair in the example would be worthwhile?
  - barking 14y ago
    You seem to have missed the part where the extreme example is not real life Actually, I referred to your example as both 'extreme' and 'artificial' in my previous post. Since the example was constructed to make your point as obvious as possible I was just pointing out that in fact P(B|A) was actually useful even in that example. Sorry for the delay in responding, I gave up yesterday because there was no option to reply even after a very long time.