Suppose that we specify beliefs about a quantity, X, then adjust these beliefs by observation on a collection of quantities, D. When we observe the actual data values,
then we may evaluate the random quantity 
. The value which is obtained
is denoted by 
. We apply the standardisation operation to ,
defining the standardised adjustment as
The value of 
may suggest that our beliefs about X appear to
be more or less affected by the data than we had expected. Very large changes
may raise the possibility that we have been overly confident in describing our
uncertainty, very small changes that we have been overly modest in valuing our
prior knowledge about the value of X.
Such diagnostics provide us with qualitative and quantitative information. If our observations suggest to us substantially new beliefs, then presumably it will be of interest to us to know this. (For example, we may appear to have made a great discovery simply because of a blunder in our programming). Even when no simple explanation of a possible discrepancy occurs to us, it will usually be of interest to identify which aspects of our beliefs have changed by substantially less or more than we had expected. Such diagnostics are of particular importance when we make very large collections of belief adjustments, so that we need simple, automatic methods to call our attention to particular assessments which we might usefully re-examine.