We now examine results summarising uncertainties within the entire
belief structure . 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 it
. 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:
The most useful result is the resolution of the belief structure:
showing that uncertainty over the entire belief structure is
only reduced by about 17%.