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    Re: On LOPs
    From: Herbert Prinz
    Date: 2002 Apr 16, 18:12 +0000

    Hi Steven,
    The "true" shape of a confidence region can be defined via a
    minumum-criterion. It would be insufficient to solve for just any odd region
    that contains the MPP with a given probability.
    For example: I am sailing towards New York Harbor and somehow I convince
    myself that I am within a radius of 5 miles of Ambros Light with 95%
    probability. Thus my 95%-confidence-area is a circle of 80 square miles. I
    could add to this area the whole City of Vienna without changing the 95% level
    significantly. But this would dilute the information contents of my result
    significantly. One useful criterion therefore might be to look for the
    _smallest_ area that contains my MPP with a given probability. (There may be
    others, particularly if certain positions are less desirable than others.) The
    locus of equal probability density is an ellipse, from which follows that the
    ellipse satisfies said minimum criterion.
    Best regards,
    Steven Wepster wrote:
    > 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.

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