I'm comparing results from ensemble data assimilation experiments where prior ensemble members are either drawn from the same (multivariate Gaussian) distribution as a "true" variable, or from a different one. I'd like a compact way of saying that. The closest I've gotten so far is "homologous" vs "heterologous" or "analogous," borrowing from biology.

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    $\begingroup$ I.i.d.? $\endgroup$ – Alexis Jul 30 at 17:19
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    $\begingroup$ When you need a compact expression and can't find one in common use, invent one and define it for your readers. Assuming your sampling is not iid, so that this common term doesn't apply, consider "fred," as in "we'll say that two sets of results are fred when they are drawn from the same distribution and otherwise are nonfred." But you could do even better by calling this "bob" -- it's one letter shorter and has a history ;-). $\endgroup$ – whuber Jul 30 at 17:20
  • $\begingroup$ I agree with Alexis. I would use the term "identically distributed". wikipedia page $\endgroup$ – Momoemoe Jul 30 at 17:48
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    $\begingroup$ Yes, similar to iid but a bit different sense... a collection of "prior" random variables could be at once iid but also drawn from a different distribution as the "truth." Perhaps "fred." $\endgroup$ – gKhagb Jul 30 at 18:07
  • $\begingroup$ What about "with equiprobable values" (or, better, value ranges)? $\endgroup$ – Sergio Jul 30 at 18:14

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