  To investigate the robustness of the output probabilities of a Bayesian
network, a sensitivity analysis can be performed. A one-way sensitivity
analysis establishes, for each of the probability parameters of a network, a
function expressing a posterior marginal probability of interest in terms of
the parameter. Current methods for computing the coefficients in such a
function rely on a large number of network evaluations. In this paper, we
present a method that requires just a single outward propagation in a junction
tree for establishing the coefficients in the functions for all possible
parameters; in addition, an inward propagation is required for processing
evidence. Conversely, the method requires a single outward propagation for
computing the coefficients in the functions expressing all possible posterior
marginals in terms of a single parameter. We extend these results to an n-way
sensitivity analysis in which sets of parameters are studied.
