A short comment on statistical versus mathematical modelling

Abstract

While the crisis of statistics has made it to the headlines, that of mathematical modelling hasn’t. Something can be learned comparing the two, and looking at other instances of production of numbers.Sociology of quantification and post-normal science can help.

Fig. 1

Model error as ideally resulting from the superposition of two curves: (i) model inadequacy error, due to using too simple a model for the problem at hand. This term goes down by making the model more complex; (ii) error propagation, which results from the uncertainty in the input variables propagating to the model output. This term grows with model complexity. Whenever the system being modelled in not elementary, overlooking important processes leaves us on the left-hand side of the plot, while modelling hubris can take us to the right-hand side