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I've noticed a lot of questions with the tag where it clearly doesn't belong. I think this happens because naive users think all statistics is mathematical statistics.

The current usage guidance (wiki exceprt) is:

Mathematical theory of statistics, concerned with formal definitions and general results.

Should we add something to this such as "do not use this tag for general questions about statistics"?

Or would that just not work? Do we know how many people look at the tag info before adding a tag?

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    $\begingroup$ I think this tag is so broad that it is useless. As far as I am concerned, it could (and even should) be eliminated altogether. However, it has almost 4k threads so the only way to get rid of it would be through SE admin action ("tag burnination") which has never ever happened on CV so far, despite multiple requests on Meta. Therefore I suspect the tag is here to stay. Given that, I personally don't care too much about what is written in its excerpt :) It's useless anyway. $\endgroup$
    – amoeba
    May 9, 2018 at 13:11
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    $\begingroup$ We could perhaps make it a synonym of "theoretical statistics" $\endgroup$ May 9, 2018 at 16:17
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    $\begingroup$ I'm not sure "theoretical statistics" would end up working, either. I don't remember the character limit, but [mathematical-theory-of-statistics] (33 characters) seems less likely to be misused. & then to the excerpt we could add, "Don't use this tag just because you think statistics has a lot of weird math in it." $\endgroup$ May 9, 2018 at 17:01
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    $\begingroup$ I honestly don't see a problem with people "misusing" this tag, because it's so vague in the first place. What's it scope supposed to be anyway? FWIW, I'd be against renaming [mathematical-statistics] into [mathemetical-theory-of-statistics] (@gung). If people get annoyed with this tag being misused then let's get rid of it. $\endgroup$
    – amoeba
    May 9, 2018 at 20:04
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    $\begingroup$ Well, like it says in the usage guidelines "theorems and proofs". The sort of thing you'd study in a statistics course in a math department. As opposed to data analysis and such. $\endgroup$
    – Peter Flom
    May 9, 2018 at 22:14
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    $\begingroup$ I use it for proofs, because the proof tag was made a synonym of it. Other than that I do not see much use of having the tag. I would rather have some tag for algebraic proofs (usually applied on properties of estimators). $\endgroup$ May 10, 2018 at 9:36
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    $\begingroup$ Somewhat related: stats.stackexchange.com/questions/32001 $\endgroup$ May 10, 2018 at 11:23
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    $\begingroup$ I have 'mathematical-statistics' among my favorite tags and use it to track those questions which entail problems with a mathematical orientation. Personally I have mostly been doing "statistics" much on an ad-hoc basis without much regards to the classics and just applying probability-theory to the problem at hand (I feel that this custom-made approach to statistics is typical for the field of astronomy where I first encountered "statistics", in comparison to the more out of the box paved roads statistics that are made for the scientist in fields such as social and agricultural sciences). $\endgroup$ May 11, 2018 at 9:29
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    $\begingroup$ So while I "feel" that the tag 'mathematical-statistics' can be useful, I wonder how much is actually misclassified? This surprises me (but maybe I have not been paying attention to this and skipped reading the misclassified questions). I would say that we should focus on the misclassification (if this is a problem to anyone) rather than eliminating the tag altogether. $\endgroup$ May 11, 2018 at 9:32
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    $\begingroup$ @MartijnWeterings I think the tag has a bimodal distribution :-). That is, it is used by some people who are clearly very new to the field (and probably don't even know that mathematical statistics is separable from statistics, or what theorem-proof math classes are like) and those who really do want theorems and proofs. I'm not proposing eliminating it. I think it's useful. $\endgroup$
    – Peter Flom
    May 11, 2018 at 11:32
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    $\begingroup$ Mathematical-statistics might be ambiguous to novice statisticians. It might be regarded as 'any' mathematics involved in statistics (doing statistics in a mathematical way), and in the end this relates to a lot of statistics (which is about numbers after all). To the more experienced statistician 'mathematical-statistics' might be more regarded as something like mathematical foundations of statistics. So, I guess this split of interpretation might be a lead to find some good differentiation of two tags for this single tag, $\endgroup$ May 11, 2018 at 11:43
  • $\begingroup$ Personally I am a big fan of 'Edward Tufte' who is much more into visualization of statistics, and I believe that this 'visualization-topic' (or related topics) is much less covered here (which surprises me). As a result, since much on stats.stackexchange is covered by mathematics, the 'tag' might seem relatively useless (broad). So maybe (?) we could classify statistics, broadly into 'visualization', 'mathematics', 'logic/philosophy', 'experimental/practical application', 'other'? $\endgroup$ May 11, 2018 at 11:52
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    $\begingroup$ @MartijnWeterings, foundations could work, too. Nb, [mathematical-foundations-of-statistics] is 38 characters; [math-foundations-of-stats] is 25; [math-theory-of-stats] is 20. $\endgroup$ May 11, 2018 at 13:21
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    $\begingroup$ Hmmm, I suppose you're right about "foundations", @amoeba. $\endgroup$ May 11, 2018 at 13:41
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    $\begingroup$ I agree that foundations indeed doesn't sound right, but what about theoretical? [mathematical-and-theoretical-statistics] at least, I think, the tag mathematical should not be about "simple"/straight-forward applied mathematics but more about the (theoretical) background of certain mathematical constructions that are used in statistics or about the discussions of the mathematics itself in certain use of applied mathematics. $\endgroup$ May 12, 2018 at 11:15

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