3 ms·
Search "decibels" in https://www.yudkowsky.net/rational/bayes https://www.yudkowsky.net/rational/bayes for the explanation. I think you're just wrong about nee
by Strilanc 3y ago
Search "decibels" in https://www.yudkowsky.net/rational/bayes https://www.yudkowsky.net/rational/bayes for the explanation.
I think you're just wrong about needing everything to be in the form X:1 or 1:X. When I compute the ratio of 1000000:1 divided by 1:20 it gives 1000000:(1/20) then scaling both sides by the same factor gives 20000000:1.
- neilkk 3y agoYour reference definitely doesn't show a calculation of the type you are trying to do. Likelihood ratios are not the same as odds ratios; they do not have the problem I described. I would be very surprised if you can find any reference at all to the number you describe as 'evidence bits', or anything equivalent, made by anyone who can show an understanding of basic probability, statistics, or information theory. I understand how you get 20,000,000 as the answer to the calculation you carry out. My point is that that number is not meaningful in any way.
- Strilanc 3y agoWhen you apply a statistical test, the various outcomes cause Bayesian updates that correspond to adding or subtracting fixed bits of evidence. When you repeat the test (and the repetitions are independent), the amount of bits of evidence you add or subtract remain the same. In other words, focusing on bits of evidence shows Bayesian updates behave like a biased random walk under repetition of a test and allow you to compute the properties of that walk. For example, suppose you are trying to estimate how much rounding errors in a pseudo random number generator betray that it is not a true exact representation of the random process. One way to quantify this is to compute the expected bits of evidence revealed per call to the RNG.