Difference between revisions of "Prior probability"

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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]]".)
 
 
==See also==
 
 
*[[Bayes's Theorem]]
 
*[[Priors]]
 

Revision as of 10:55, 13 October 2012