When do Numbers Really Matter?
  Common wisdom has it that small distinctions in the probabilities quantifying
a Bayesian network do not matter much for the resultsof probabilistic queries.
However, one can easily develop realistic scenarios under which small
variations in network probabilities 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
analytical 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 are
also important for approximate inference algorithms that preprocessnetwork CPTs
to eliminate small distinctions in probabilities.
