  Identifiability of polynomial models is a key requirement for multiple
regression. We consider an analogue of the so-called statistical fan, the set
of all maximal identifiable hierarchical models, for cases of noisy
experimental designs or measured covariate vectors with a given tolerance
vector. This gives rise to the definition of the numerical statistical fan. It
includes all maximal hierarchical models that avoid approximate linear
dependence of the model terms. We develop an algorithm to compute the numerical
statistical fan using recent results on the computation of all border bases of
a design ideal from the field of algebra. The ideas are applied to data from a
thermal spraying process. It turns out that the numerical statistical fan is
effectively computable and much smaller than the respective statistical fan.
The gained enhanced knowledge of the space of all stable identifiable
hierarchical models enables improved model selection procedures.
