Prior probability
From Lesswrongwiki
The probability that you start with before seeing the evidence. One of the inputs into Bayes's Theorem.
Suppose there are a hundred boxes, one of which contains a diamond; and this is all you know about the boxes. Then your prior probability that a box contains a diamond is 1%, or prior odds of 1:99.
Later you may run a diamond-detector over a box, which is 88% likely to beep when a box contains a diamond, and 8% likely to beep (false positive) when a box doesn't contain a diamond. If the detector beeps, then this is evidence with a likelihood ratio of 11:1 in favor of a diamond, which sends the prior odds of 1:99 to posterior odds of 11:99 = 1:9. But if someone asks you "What was your prior probability?" you would still say "My prior probability was 1%, but I saw evidence which raised the posterior probability to 10%."
Your "prior probability" in this case was actually based on a certain amount of information - i.e., someone told you that one out of a hundred boxes contained a diamond. Indeed, someone told you how the detector worked - what sort of evidence a beep represented. For a more complicated notion of prior beliefs, including prior beliefs about the meaning of observations, see "priors". ("Prior probability" is more likely to refer to a single summary judgment of some variable's prior probability, versus a Bayesian's general "priors".)
