Bayesian Statistics by Lee Peter M

Bayesian Statistics by Lee Peter M

Author:Lee, Peter M.
Language: eng
Format: epub
ISBN: 9781118359778
Publisher: Wiley
Published: 2012-06-13T16:00:00+00:00

where V(F) is the volume of the hyperellipsoid E(F). At first sight it appears that this is I-dimensional, but because it represents the intersection of a hyperellipsoid in I dimensions with a hyperplane through its centre, which is a hyperellipsoid in (I–1) dimensions. If this is not clear, it may help to note that an ordinary sphere in three-dimensional space cuts a plane in a circle, that is, a sphere in 3–1=2 dimensions. It follows that

and hence

It follows that the density of is proportional to


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