Each evaluation that we have so far discussed assesses the change in belief for
a single element of 
. We now summarise our overall changes in belief over
, relative to our prior uncertainty. We make the following definition.
Definition The size of the adjustment of B given D=d is
Note: There are various alternative scalings for the changes in belief which we can choose, each of which may be analysed in a similar fashion to our suggested choice and provide useful insights into the belief revision. Our particular choice leads to the construction of various quantities whose properties unify many of the interpretive and diagnostic features of the belief revision, and is particularly helpful when we come to consider the adjustment of beliefs in stages.
We now identify the element, 
, of with the largest such
change in expectation. is termed the bearing for the
adjustment, and is constructed as follows.
Definition The bearing for the adjustment of the belief structure
by observation of D=d is the element in defined by
where 
are any collection of elements of
which are a priori uncorrelated, with variance one. (The canonical components
of 
form one such collection and the canonical directions for the
adjustment form another when suitably scaled. does not depend on the choice of .)
The bearing is so named as it expresses both the direction and the magnitude of the change between prior and adjusted beliefs, as follows:
, 
;
, then a bearing of 
would
represent 
times the change in expectation as would a bearing of
, for every element of . 
We may therefore deduce that is indeed the direction of
maximum change in belief, and that
