  A wide array of graphical models can be parametrised to have atomic
probabilities represented by monomial functions. Such monomial structure has
proven very useful when studying robustness under the assumption of a
multilinear model where all monomial have either zero or one exponents.
Robustness in probabilistic graphical models is usually investigated by varying
some of the input probabilities and observing the effects of these on output
probabilities of interest. Here the assumption of multilinearity is relaxed and
a general approach for sensitivity analysis in non-multilinear models is
presented. It is shown that in non-multilinear models sensitivity functions
have a polynomial form, conversely to multilinear models where these are simply
linear. The form of various divergences and distances under different
covariation schemes is also formally derived. Proportional covariation is
proven to be optimal in non-multilinear models under some specific choices of
varied parameters. The methodology is illustrated throughout by an educational
application.
