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What is the difference between (probability) and (probability-theory)? If there is none, is it better to use both tags or to decide on one (by tossing a fair coin, of course)?

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I view the "probability" tag for questions in which one wants a probability or expected value calculated. A classic example would be this one: If a 1 meter rope is cut at two uniformly randomly chosen points (to give three pieces), what is the average length of the smallest piece?

I view the "probability theory" tag for questions about, well, the theory of probability, such as a question about sigma-algebras, or how Lebesgue measure is used to define expectation, such as this one: Lebesgue integral basics.

Obviously there would be some overlap at the boundary between the two tags as I have defined them. A rough analogy would be the difference between the "calculus" and "real analysis" tags.

The user base currently seems to use these tags interchangeably rather than the way I have defined them. (In fact, the Lebesgue integral question is actually tagged "probability" rather than "probability theory.") But if people like my distinction we could codify it in the tag wikis, and then hopefully the user base would eventually converge to using these tags this way.

(While I would prefer this to be the solution, I don't feel strongly enough about it to argue too much if everyone else prefers to merge the two tags. I would also be interested to hear the opinions of the other people who are active in these two tags.)

Update: Since the community seems to be in support of this view, I have requested that these changes be made to the probability and probability-theory tag wikis, and these changes have been accepted. With respect to Willie Wong's comment, we'll have to see how well new question askers follow this convention.

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    $\begingroup$ In principle I agree with your proposal. But I feel that trying to codify this difference is swimming against the current, fighting an uphill battle etc. I'm already rather pessimistic about the number of people who read the FAQ; I'm even more so about the number of people who read the tag-wikis. $\endgroup$ – Willie Wong Feb 21 '11 at 11:00
  • $\begingroup$ Actually, this is the same impression I got from perusing the questions in both tags (though it was not always followed). $\endgroup$ – Akhil Mathew Feb 22 '11 at 1:38
  • $\begingroup$ I just changed the tag on the Lebesgue integral question to "probability-theory." $\endgroup$ – Mike Spivey Feb 23 '11 at 6:34
  • $\begingroup$ This is more or less what I'd thought and more or less how I'd been retagging things earlier on. Yes, new people don't know how to tag—that's why higher rep people can retag. $\endgroup$ – Isaac Feb 23 '11 at 23:06
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Looking at these tags now 5 months later, it seems they're still quite thoroughly mixed up: is full of basic questions about calculating expected values etc., while contains many advanced and theoretical questions that should probably go under -theory under Mike's convention.

So I'd like to revive this discussion: should we merge probability-theory into probability, or is this just a case of needing more aggressive retaggers?

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  • $\begingroup$ The main problem is that the "retaggers" don't read the Tags Wiki either. For smaller issues I've been doing some manual clean-up in the past weeks (for example, (roots) recently). In the particular case of probability versus probability theory, manual retagging will flood hundreds of questions to the front page (as opposed to a small handful), and I am not convinced that in this case it is worth the effort. $\endgroup$ – Willie Wong Jul 25 '11 at 17:38
  • $\begingroup$ Let me explain my first sentence in the previous comment a bit all. Unless you were involved in this discussion, or you happened to hover your mouse over the tag to read the tag wiki, seeing a question on Tchebyshev's inequality tagged as (probability) would not be too out of place. Some other tags that are similarly vague and unsuitable are (analysis) and (algebra). In an ideal world such vague tags should not have been allowed in the first place. But it is rather impractical to deal with them now. $\endgroup$ – Willie Wong Jul 25 '11 at 17:42
  • $\begingroup$ It would be nice if there is some convenient way for moderators to split a tag... $\endgroup$ – Willie Wong Jul 25 '11 at 17:44

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