  Sensitivity analysis (SA) has much to offer for a very large class of
applications, such as model selection, calibration, optimization, quality
assurance and many others. Sensitivity analysis offers crucial contextual
information regarding a prediction by answering the question "Which uncertain
input factors are responsible for the uncertainty in the prediction?" SA is
distinct from uncertainty analysis (UA), which instead addresses the question
"How uncertain is the prediction?" As we discuss in the present paper much
confusion exists in the use of these terms. A proper uncertainty analysis of
the output of a mathematical model needs to map what the model does when the
input factors are left free to vary over their range of existence. A fortiori,
this is true of a sensitivity analysis. Despite this, most UA and SA still
explore the input space; moving along mono-dimensional corridors which leave
the space of variation of the input factors mostly unscathed. We use results
from a bibliometric analysis to show that many published SA fail the elementary
requirement to properly explore the space of the input factors. The results,
while discipline-dependent, point to a worrying lack of standards and of
recognized good practices. The misuse of sensitivity analysis in mathematical
modelling is at least as serious as the misuse of the p-test in statistical
modelling. Mature methods have existed for about two decades to produce a
defensible sensitivity analysis. We end by offering a rough guide for proper
use of the methods.
