3 ms·

I actually thought it was the worst part of the article because it fails to put the statements into context. Let me quote from "0 And 1 Are Not Probabilities"[

I actually thought it was the worst part of the article because it fails to put the statements into context. Let me quote from "0 And 1 Are Not Probabilities"[1]. > In probabilities, 0.9999 and 0.99999 seem to be only 0.00009 apart, so that 0.502 is much further away from 0.503 than 0.9999 is from 0.99999. To get to probability 1 from probability 0.99999, it seems like you should need to travel a distance of merely 0.00001. > But when you transform to odds ratios, 0.502 and 0.503 go to 1.008 and 1.012, and 0.9999 and 0.99999 go to 9,999 and 99,999. And when you transform to log odds, 0.502 and 0.503 go to 0.03 decibels and 0.05 decibels, but 0.9999 and 0.99999 go to 40 decibels and 50 decibels. > When you work in log odds, the distance between any two degrees of uncertainty equals the amount of evidence you would need to go from one to the other. That is, the log odds gives us a natural measure of spacing among degrees of confidence. [1]: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar... Edit: formatting

mattkrause 7y ago
The quoted part is sensible, but the title is goofy. Zero and one have to be probabilities. A lot of the underlying math doesn't work out otherwise, but you can also believe something always/never happens (if you're a Bayesian), or observe the same thing happening over and over again (for the frequentists). Your example shows that (non-linear) transformations aren't linear, and that our gut feels about likelihood aren't either, which is true enough. However, you wouldn't say "101 ˚C isn't a temperature" because it takes much less energy to heat a wet thing from 97 to 99˚ than it does to bring it from 99 to 101˚ because of the phase change.
- marcosdumay 7y ago
  You can not ever discover in a statistical test that some probability is 0 or 1. Those are impossible values. You can get arbitrarily close to them, but you can never reach those values. Of course, they are valid values for the set of probabilities, just like 0K is a valid temperature, and c is a valid speed for massive things. You just will never see any of those.
  - dragonwriter 7y ago
    > You can not ever discover in a statistical test that some probability is 0 or 1 Sure you can: if you are using inferential statistics and trying to determine the population incidence of some trait and every sample has a sample incidence of exactly 1 then the population estimate will be exactly 1. And that works the same way for 0, or any other value, too. > c is a valid speed for massive things. No, it's not. An object with any rest mass would require infinite energy to reach c. It's an excluded upper bound, not a valid speed.
  - mattkrause 7y ago
    No, the issue you’re referring to applies to anything estimated directly from a sample; there’s nothing magic about zero or one. If you see 5000/10000 heads, the maximum likelihood estimate for that proportion is 0.5, but it still has some uncertainty attached: the 95% CI is about [0.49, 0.51]. With more data, you can shrink that interval, but you can never collapse it completely. On the other hand, that same data does let you assign exactly zero probability to the hypotheses “the coin is all heads” and “both sides of the coin are tails”, since you’ve seen counterexamples of both.

mattkrause 7y ago

The quoted part is sensible, but the title is goofy. Zero and one have to be probabilities. A lot of the underlying math doesn't work out otherwise, but you can also believe something always/never happens (if you're a Bayesian), or observe the same thing happening over and over again (for the frequentists). Your example shows that (non-linear) transformations aren't linear, and that our gut feels about likelihood aren't either, which is true enough. However, you wouldn't say "101 ˚C isn't a temperature" because it takes much less energy to heat a wet thing from 97 to 99˚ than it does to bring it from 99 to 101˚ because of the phase change.

marcosdumay 7y ago
You can not ever discover in a statistical test that some probability is 0 or 1. Those are impossible values. You can get arbitrarily close to them, but you can never reach those values. Of course, they are valid values for the set of probabilities, just like 0K is a valid temperature, and c is a valid speed for massive things. You just will never see any of those.
- dragonwriter 7y ago
  > You can not ever discover in a statistical test that some probability is 0 or 1 Sure you can: if you are using inferential statistics and trying to determine the population incidence of some trait and every sample has a sample incidence of exactly 1 then the population estimate will be exactly 1. And that works the same way for 0, or any other value, too. > c is a valid speed for massive things. No, it's not. An object with any rest mass would require infinite energy to reach c. It's an excluded upper bound, not a valid speed.
- mattkrause 7y ago
  No, the issue you’re referring to applies to anything estimated directly from a sample; there’s nothing magic about zero or one. If you see 5000/10000 heads, the maximum likelihood estimate for that proportion is 0.5, but it still has some uncertainty attached: the 95% CI is about [0.49, 0.51]. With more data, you can shrink that interval, but you can never collapse it completely. On the other hand, that same data does let you assign exactly zero probability to the hypotheses “the coin is all heads” and “both sides of the coin are tails”, since you’ve seen counterexamples of both.