  Common wisdom has it that small distinctions in the probabilities
(parameters) quantifying a belief network do not matter much for the results of
probabilistic queries. Yet, one can develop realistic scenarios under which
small variations in network parameters can lead to significant changes in
computed queries. A pending theoretical question is then to analytically
characterize parameter changes that do or do not matter. In this paper, we
study the sensitivity of probabilistic queries to changes in network parameters
and prove some tight bounds on the impact that such parameters can have on
queries. Our analytic results pinpoint some interesting situations under which
parameter changes do or do not matter. These results are important for
knowledge engineers as they help them identify influential network parameters.
They also help explain some of the previous experimental results and
observations with regards to network robustness against parameter changes.
