Sensitivity analysis, multilinearity and beyond
  Sensitivity methods for the analysis of the outputs of discrete Bayesian
networks have been extensively studied and implemented in different software
packages. These methods usually focus on the study of sensitivity functions and
on the impact of a parameter change to the Chan-Darwiche distance. Although not
fully recognized, the majority of these results heavily rely on the multilinear
structure of atomic probabilities in terms of the conditional probability
parameters associated with this type of network. By defining a statistical
model through the polynomial expression of its associated defining conditional
probabilities, we develop a unifying approach to sensitivity methods applicable
to a large suite of models including extensions of Bayesian networks, for
instance context-specific and dynamic ones, and chain event graphs. By then
focusing on models whose defining polynomial is multilinear, our algebraic
approach enables us to prove that the Chan-Darwiche distance is minimized for a
certain class of multi-parameter contemporaneous variations when parameters are
proportionally covaried.
