Each prior statement that we make describes our beliefs about some random quantity. When we actually observe this quantity, we may compare what we expect to happen with what actually happens. A simple comparison is as follows.
For a single random quantity X, suppose that we specify 
and 
and
then observe value x. Using only our limited belief specification, we evaluate the standardised observation defined as
has prior expectation zero and prior variance one. Thus, a very
large absolute value for might suggest that we have misspecified
or underestimated the variability of X, or misrecorded the value x, while a
value near zero might suggest that we have overestimated the variability of
X. How large or small must be to merit attention depends entirely upon
the context, relating in large part to our confidence in our prior formulation.