As we think about drawing conclusions about the physical world,
we come to realize that everything we do is based on what we
know about the world. Conclusions about hypotheses will
be based on our general background knowledge.
To emphasize the dependence of probability on the state of
background information, which we designate as , we will make
it explicit by writing
, rather than simply .
(Note that, in general,
if and are different states of information.)
For example, Eq. (4) should be more precisely