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

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... 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.