  In the absence of any compelling physical model, cosmological systematics are
often misrepresented as statistical effects and the approach of marginalising
over extra nuisance systematic parameters is used to gauge the effect of the
systematic. In this article we argue that such an approach is risky at best
since the key choice of function can have a large effect on the resultant
cosmological errors. As an alternative we present a functional form filling
technique in which an unknown, residual, systematic is treated as such. Since
the underlying function is unknown we evaluate the effect of every functional
form allowed by the information available (either a hard boundary or some
data). Using a simple toy model we introduce the formalism of functional form
filling. We show that parameter errors can be dramatically affected by the
choice of function in the case of marginalising over a systematic, but that in
contrast the functional form filling approach is independent of the choice of
basis set. We then apply the technique to cosmic shear shape measurement
systematics and show that a shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is
required for a future all-sky photometric survey to yield unbiased cosmological
parameter constraints to percent accuracy. A module associated with the work in
this paper is available through the open source iCosmo code available at
http://www.icosmo.org .
