3 ms·

The problem with it is that layman people believe that both of these statements are equal to "it's a 999/1000 chance that it was something else". Which is not t

The problem with it is that layman people believe that both of these statements are equal to "it's a 999/1000 chance that it was something else". Which is not true. The difference in these two formulations is that for b) it's explicit wrong, for a) this is arguably what the article says (which is not what the scientists say)

simiones 6y ago
The article can be read as "there is a 999/1000 chance that this is not a coincidence". This is strictly speaking correct, because it doesn't specify what the coincidence would be. The correct interpretation is "there is a 999/1000 chance that you wouldn't see this data if the particle didn't exist" / "there is a 1/1000 chance that you would see this data if the particle didn't exist". The wrong interpretation that still agrees with the statement is "there is a 999/1000 chance that the particle exists given that we have seen this data" / "there is a 1/1000 chance that the particle doesn't exist given that we have seen this data". P(data | no particle) = P (no particle | data) * P (data) / P (no particle). As a layman, I have no idea what P(data) is, and I think no one can give a convincing estimate for P(no particle). Since P(data | no particle) and P(no particle | data) are in fact proportional, the only thing I should really care about as a layman is the value of any one of them. I any way can't evaluate myself what would be a convincing probability, since I don't have any proper priors.
- davrosthedalek 6y ago
  No, not quite. The probability that this is not a coincidence is unknown. The probability that you SAW the data if the particle didn't exist is 100%. The probability that you will not see it /again/ is 999/1000. The probabilities 1/1000 (or 999/1000) are only meaningul probabilites for something in the world where in fact it was a coincidence. In any other world, they are not. So saying "there is a 999/1000 chance that this is not a coincidence" isn't true, as the calculation of 999/1000 must assume that it fact it IS a coincidence.

simiones 6y ago

The article can be read as "there is a 999/1000 chance that this is not a coincidence". This is strictly speaking correct, because it doesn't specify what the coincidence would be. The correct interpretation is "there is a 999/1000 chance that you wouldn't see this data if the particle didn't exist" / "there is a 1/1000 chance that you would see this data if the particle didn't exist". The wrong interpretation that still agrees with the statement is "there is a 999/1000 chance that the particle exists given that we have seen this data" / "there is a 1/1000 chance that the particle doesn't exist given that we have seen this data". P(data | no particle) = P (no particle | data) * P (data) / P (no particle). As a layman, I have no idea what P(data) is, and I think no one can give a convincing estimate for P(no particle). Since P(data | no particle) and P(no particle | data) are in fact proportional, the only thing I should really care about as a layman is the value of any one of them. I any way can't evaluate myself what would be a convincing probability, since I don't have any proper priors.

davrosthedalek 6y ago
No, not quite. The probability that this is not a coincidence is unknown. The probability that you SAW the data if the particle didn't exist is 100%. The probability that you will not see it /again/ is 999/1000. The probabilities 1/1000 (or 999/1000) are only meaningul probabilites for something in the world where in fact it was a coincidence. In any other world, they are not. So saying "there is a 999/1000 chance that this is not a coincidence" isn't true, as the calculation of 999/1000 must assume that it fact it IS a coincidence.