bad fit - nomenclature for breeds Question:
What is it called when one uses a basis, like the pure line instead of the sigmoid/logistic, in a manner that grossly departs from the "physics" of the problem?  There should be a word for that.  
Humorous introduction:
Lots of physics and engineering is about "modeling a cow as a sphere" (or spheres).  Moo, moo, moo .  
It has been said that "All models are wrong, but some are useful". 
Examples:
Using a pure line model in place of a sigmoid function can be useful in a subset of the domain, but outside of that limited range, they depart from the "physics" of the problem.  If they are made piecewise, the departure and error can be reduced.  
In Galerkin approximation for PDE's the same problem arises.  If a piecewise basis that departs "more" from the physics is used, that is compensated for by much higher levels of discretization in the domain.  The use of basis functions that can work in other dimensions, account for other loads, and handle higher order functions (polynomial, radial, etc) can allow adequate representation with reduced discretization.
There should be a clean and efficient vocabulary that allows handling of the departures of the model from the reality.  This is complicated by the requirement of standing them on top of an existing language.  
Current Similar words 


*

*Under-discretization is what happens when there are too few piecewise samples to adequately represent the phenomena.

*Over-discretization is what happens when there are too many piecewise chunks and it adds heavy computational burden, or spurious numeric phenomena.


The question again:
Neither of these address the match between a single basis element and the "physics" or "phenomenology" of the problem.  What does?
 A: The most efficient method of classifying such things is merely stating that inappropriate or spurious basis functions are inefficient in that they have properties that are undesirable, for example, they fit the data poorly, and if a more inclusive attempt to span the data using more parameters of that basis is attempted the results have parameters the partial probability for which ANOVA or other testing suggests are supernumerary parameters. 
That is, spurious basis functions are identified by their inefficiency in the sense of Ockham's razor. Also, a correct set of basis functions for a space spans that space in the sense that a linear combination of those basis functions can exactly express any object in that space, e.g., waveforms are spanned by sums of phase shifted sin waves, quadratics are spanned by $1,\; t,\; t^2.$ One can also distinguish cardinal basis functions, e.g., $1,\; t,\; t^2,$  for quadratics from other quadratic spanning basis functions; e.g., $\sqrt{2},\; \pi t,\; e\,t^2.$
