Bayes linear methods are basically intended for large problems: particularly those that are too big to analyse using a fully specified Bayesian approach. We have chosen for our illustration a small example to keep things simple. Indeed, this simple example is extracted from a very much larger and more complicated problem that we mean to present elsewhere. We intend also to present elsewhere explicit consideration of the belief elicitation process which gave rise to the specifications used here.
In practice, our analysis could take into account the way in which the
covariance specifications were produced. For example, our Doctor thought
about various underlying quantities such as differences between herself
and a young patient. At a later stage, it may then prove possible to
return to the way in which the beliefs were generated in order to
address queries raised during the general analysis. For example, if the
analysis suggests the possibility that she specified too tight a variance
for 
, say, then she may be able to return to the way in which
she constructed this variance, and then perhaps to discover a flawed
specification for some underlying quantity that she used in the
construction. However, whilst valuable, this would overcomplicate our
elementary example, and so we omit such considerations.