We can ignore because
it is independent of and fixed for our given and T.
It has the practical point that Likelihood is never normalized
sensibly.
philosophically represents a priori
knowledge of before experiment (measurement of )
performed.
This is shaky---not because we don't really know how to define
what |T (``given T'') means---but, for instance, suppose we wish to
parameterize ``complete ignorance'' of before experiment
performed.