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Wow. Thank you for the very informative comments, quid! You should've posted it as an answer. The general asymptotic case is as exciting as it is difficult, but I'm also interested in non-asymptotic results. So results on some restricted $n$ and computational math things are great, too. About the last sentence of your comment, you're still mad at me, aren't ya?
The discussion Joel gave a link got an accepted answer, which links to an article in the Journal of Applied Statistics tandfonline.com/doi/abs/10.1080/02664760120074960 To my totally untrained layman's eye, the abstract seems to suggest the article might lead to or help to find some sort of answer to TB's original question.
I apologize for the multiple edits to this post in a short span of time, which might have unnecessarily pushed up this thread to the top of the front page. I promise I'll be more careful next time.
I don't want to spread the wrong information or get own'd by experts. But the linked blog post by Terence Tao mentions applications to astronomy. You can find a bunch of papers mentioning telescopes and whatnot by casual googling too, e.g., dx.doi.org/10.1109/JSTSP.2008.2005337
@Yemon Yes, it is. The gullible are also at falt, though. Banning information too much or forbidding discussions too quickly because it's potentially dangerous isn't going to fly in a democratic community, in my opinion.
Look, folks. This is what you get for using a weak key for your public-key chryptography when you're surrounded by mathematicians. (Dear diary, Thomas is a meanie. A biiig meanie!)