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That's analagous to saying it's a problem that Health screenings are often targeted at high-risk groups when the vast majority of those groups won't get the dis

by barking 14y ago

That's analagous to saying it's a problem that Health screenings are often targeted at high-risk groups when the vast majority of those groups won't get the disease in any case.

jlgreco 14y ago
.....and, where the cost of false positives is sufficiently high and the rate of false positives is sufficiently high, that is a very relevant consideration that is in fact made by the medical community. That is just a basic of modern medicine. The world is not black and white. These are things that must be weighed and considered rationally with real data, not emotionally with fabricated absolutes. You don't get to discard half of your equation because when you include it the results don't make you feel warm and fuzzy. P(A|B) = \frac{P(B | A)\, P(A)}{P(B)} Not a hard concept.
- barking 14y ago
  I'm sorry but you have gone off on a tangent there. We weren't arguing about the effectiveness of the policy just the rationale behind it, I believe. I don't have any stats on that, do you?
  - jacquesm 14y ago
    You were never arguing. You were being educated.
    - deleted 14y ago
      [deleted]
  - jlgreco 14y ago
    A rationale that includes P(B|A) but not P(A|B) is not a rational one. I have been asking you to evaluate the legitimacy of the rationale by considering P(A|B).
    - 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?
  - nitrogen 14y ago
    Effectiveness is the only rationale that should matter. Also, you might benefit from having a look around http://lesswrong.com/ http://lesswrong.com/; many of the arguments you will see on HN are grounded in the concepts of Bayesian rationality described there.
    - barking 14y ago
      Thanks for the link, I'll have a look at it. What I meant by rationale was the reasoning behind the policy, it's actual effectiveness would, I guess, only become apparent in practice.
deleted 14y ago
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by barking 14y ago

That's analagous to saying it's a problem that Health screenings are often targeted at high-risk groups when the vast majority of those groups won't get the disease in any case.

jlgreco 14y ago

.....and, where the cost of false positives is sufficiently high and the rate of false positives is sufficiently high, that is a very relevant consideration that is in fact made by the medical community. That is just a basic of modern medicine. The world is not black and white. These are things that must be weighed and considered rationally with real data, not emotionally with fabricated absolutes. You don't get to discard half of your equation because when you include it the results don't make you feel warm and fuzzy. P(A|B) = \frac{P(B | A)\, P(A)}{P(B)} Not a hard concept.

barking 14y ago
I'm sorry but you have gone off on a tangent there. We weren't arguing about the effectiveness of the policy just the rationale behind it, I believe. I don't have any stats on that, do you?
- jacquesm 14y ago
  You were never arguing. You were being educated.
  - deleted 14y ago
    [deleted]
- jlgreco 14y ago
  A rationale that includes P(B|A) but not P(A|B) is not a rational one. I have been asking you to evaluate the legitimacy of the rationale by considering P(A|B).
  - 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?
- nitrogen 14y ago
  Effectiveness is the only rationale that should matter. Also, you might benefit from having a look around http://lesswrong.com/ http://lesswrong.com/; many of the arguments you will see on HN are grounded in the concepts of Bayesian rationality described there.
  - barking 14y ago
    Thanks for the link, I'll have a look at it. What I meant by rationale was the reasoning behind the policy, it's actual effectiveness would, I guess, only become apparent in practice.

deleted 14y ago

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