A natural diagnostic for assessing the magnitude of an adjustment is to compare the largest standardised change in expectation that we observe to our expectation for the magnitude of the largest change, evaluated prior to observing D. This expectation is assessed as follows.
( is the random element of
which takes the value
if D takes value d.) Thus, the expected size of the adjustment is equal to
the resolved uncertainty for the structure. To compare the observed and expected values, we
define the size ratio for the adjustment of B by D to be
We anticipate that the ratio will be near one. Large values of the size ratio suggest that we have formed new beliefs which are surprisingly discordant with our prior judgements. Values near zero might suggest that we have exaggerated our prior uncertainty.
The size ratio is essentially a ratio of variances. To determine some `critical
size' for this quantity, we would, at the least, need to assess the variance of
our variance statements, i.e. to make fourth moment specifications. For the
present, we treat the ratio as a simple warning flag drawing our attention to
possible conflicts between prior and adjusted beliefs.