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Adjusting a collection of quantities

 

We now examine results summarising uncertainties within the entire belief structure tex2html_wrap_inline8554 . By convention we take the initial uncertainty in the belief structure to be the rank of the variance matrix associated with it: the maximal number of mutually uncorrelated quantities in the structure according to the covariances expressed over itgif. We obtain the adjusted uncertainty for the structure essentially by adding the adjusted variances for these uncorrelated quantities (scaled to have prior variance unity). We take the resolved uncertainty to be the difference between the initial and adjusted uncertainty, and the resolution for the belief structure follows analagously with that for individual elements as the ratio of resolved to initial uncertainty. Hence our initial, adjusted and resolved uncertainties for the entire belief structure are:

eqnarray736

The most useful result is the resolution of the belief structure:

displaymath8916

showing that uncertainty over the entire belief structure tex2html_wrap_inline8554 is only reduced by about 17%.



David Wooff
Thu Oct 15 12:20:04 BST 1998