  In this paper we revisit the well-known technique of predicate abstraction to
characterise performance attributes of system models incorporating probability.
We recast the theory using expectation transformers, and identify transformer
properties which correspond to abstractions that yield nevertheless exact bound
on the performance of infinite state probabilistic systems. In addition, we
extend the developed technique to the special case of "data independent"
programs incorporating probability. Finally, we demonstrate the subtleness of
the extended technique by using the PRISM model checking tool to analyse an
infinite state protocol, obtaining exact bounds on its performance.
