NavList:

   

Reply

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,

Herbert

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.

   

Reply