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    Re: Precision of lunars
    From: Alexandre Eremenko
    Date: 2007 Apr 26, 10:41 -0400

    Dear Frank,
    > I guess the only part I'm puzzled by now is why you agreed with Lord
    > Kelvin
    > that one could not expect better than 0.5 minute of arc accuracy?
    Well one has to be very careful with the terms when one speaks of
    accuracy. See the excellent discussion of the matter in Kalivoda's
    message. Just how do we reduce a raw of errors of 100 shots
    to one number which "characterizes accuracy".
    One can talk of "average absolute error" or a "median absolute error".
    Or that 95% of all shots have the error less than ... and so on.
    Let's take my data, as an example. You see that about 70% of the shots
    are within 0.2' of the truth. But still the errors of 0.5'
    occur, and these are not blunders. And these could not be removed
    by the averaging at the time of the observation. Now suppose I
    am really in a situation
    where my life depends on the knowledge of my position.
    I make a series of 6 shots. It is LIKELY that it is within 0.2'
    of the truth, but certainly will not BET on it.
    I cannot "EXPECT that they
    are better than within 0.5' ".
    Im other words, I believe Kelvin does not speak
    of "sigma" but speaks of
    "3 sigma" in his talk.
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