  We consider a problem of extrapolating the collision properties of a large
polyatomic molecule A-H to make predictions of the dynamical properties for
another molecule related to A-H by the substitution of the H atom with a small
molecular group X, without explicitly computing the potential energy surface
for A-X. We assume that the effect of the $-$H $\rightarrow$ $-$X substitution
is embodied in a multidimensional function with unknown parameters
characterizing the change of the potential energy surface. We propose to apply
the Gaussian Process model to determine the dependence of the dynamical
observables on the unknown parameters. This can be used to produce an interval
of the observable values that corresponds to physical variations of the
potential parameters.
  We show that the Gaussian Process model combined with classical trajectory
calculations can be used to obtain the dependence of the cross sections for
collisions of C$_6$H$_5$CN with He on the unknown parameters describing the
interaction of the He atom with the CN fragment of the molecule. The unknown
parameters are then varied within physically reasonable ranges to produce a
prediction uncertainty of the cross sections. The results are normalized to the
cross sections for He - C$_6$H$_6$ collisions obtained from quantum scattering
calculations in order to provide a prediction interval of the thermally
averaged cross sections for collisions of C$_6$H$_5$CN with He.
