Consider a situation where a person has partial knowledge, but we have a more complete picture. For example, suppose that we want to know the probability that a fish is red. Suppose that the person with partial information knows 1/3 of all fish are red, but we know that the particular species is actually red 2/3 of the time. Do these two separate probabilities have special names? If they don't have any standard names, what would you call them?
Terminology for handling probabilities with partial knowledge
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terminology
probability
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0@Casebash: it seems there are several different concepts expressed in the question: (1) states of knowledge, levels of information, degrees of evidence, etc together with a (partial) ordering where some states are "more complete" than others, (2) assignment of probability models based on states of knowledge (and possibly also based on other things that are assigner-dependent), and (3) a "true" probability model that the assignments might converge to as the state of knowledge becomes increasingly complete. Concepts and setting of statistics (esp. inference) are highly relevant here. – 2010-09-14
2 Answers
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They are called "personal probabilities" in the literature on Bayesian statistics, which is the field where the possibility of different probability assessments among different observers is considered. You could check out the Wikipedia article on Bayesian probability, for instance.
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0@T: I won't disagree. In the back of my mind, though, is the thought that a search on "personal probability" would be much more fruitful than a search on "different" or even "different probability" ;-). – 2010-09-11
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I would call the second of these a conditional probability when trying to emphasise the difference:
The probability of a chosen fish being red is 1/3.
The conditional probability of a fish being red, given that it is species X, is 2/3.
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0That isn't quite it – 2010-09-08