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    Re: On LOPs
    From: Steven Wepster
    Date: 2002 Apr 16, 15:29 +0200

    Let me add one cent. I don't understand what _the_ _true_ form of a
    confidence region should mean.  IMO a confidence region is a region that
    contains the MPP with a specified probability, often taken as 95%. It can
    be circular, elliptical, square, heart-shaped or whatever you prefer, for
    whatever theoretical, practical, or other reasons are important to you.
    I have no references at hand now, but I remember there is a chapter on
    statistical navigation in Bowditch (at least in my eighties edition). I've
    never read it because I know I will never figure out an error ellipse in a
    force six on a dark night in Dover Strait.
    Steven Wepster                          wepster@math.uu.nl
                                            tel +31 30 253 1531
    Mathematisch Instituut
    Universiteit Utrecht
    PO Box 80.010
    3508 TA Utrecht
    The Netherlands
    >With respect, you have not advanced any logical reason why these
    >confidence intervals should be elliptical and (as I implied yesterday) a
    >brief graphical examination of the problem suggests that they are not
    >once there are more than two LOPs involved. What you appear to have is a
    >programmed version of some (unknown and thus unverifiable) equations
    >that calculate an elliptical approximation to the true shape of the
    >confidence interval. That makes yours one step more realistic than an
    >assumption that the area of uncertainty is circular but it does not
    >demonstrate that the true confidence intervals are elliptical.

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