  Studying the effects of one-way variation of any number of parameters on any
number of output probabilities quickly becomes infeasible in practice,
especially if various evidence profiles are to be taken into consideration. To
provide for identifying the parameters that have a potentially large effect
prior to actually performing the analysis, we need properties of sensitivity
functions that are independent of the network under study, of the available
evidence, or of both. In this paper, we study properties that depend upon just
the probability of the entered evidence. We demonstrate that these properties
provide for establishing an upper bound on the sensitivity value for a
parameter; they further provide for establishing the region in which the vertex
of the sensitivity function resides, thereby serving to identify parameters
with a low sensitivity value that may still have a large impact on the
probability of interest for relatively small parameter variations.
