Applied Mathematics and Statistics are Not the Same!

Applied mathematics is not statistics. And vice versa.

Personally, I think this is an obvious statement, but at least one prominent sexy journal (Proceedings of the National Academy of Sciences) does not get it, and in my opinion this leads to a rather unfair bias against applied mathematics in this journal. Take a look at PNAS's editorial board, and in particular take a look at the three scholars listed under the category "Applied Mathematical Sciences". All three of them --- Peter Bickel, David Donoho, and Stephen Fienberg --- are card-carrying statisticians.

This is a major inequity. (I think it's also a major problem, but instead of arguing that per se, let me instead argue the lesser claim that it's a major inequity.) For example, applied mathematicians and statisticians have completely different notions of the word "model". To a typical applied mathematician, modelling constitutes the development of dynamical and/or generative models. A model might be a set of coupled differential equations that is derived using momentum balances and constitutive laws, it might be a phenomenological set of differential or difference equations that attempts to describe some qualitative features in a biological system, it might be a set of rules for generating an ensemble of random graphs, etc. Wikipedia has a long discussion of what constitutes a mathematical model, and many of these are the "dynamical models" that have long been favored by applied mathematicians. A statistical model, however, is something completely different. The phrasing in Wikipedia states that a statistical model "describes how one or more random variables are related to one or more random variables." Clearly, the Navier Stokes equations do not constitute a statistical model; but they are a mathematical model.

So why am I ranting about the inequity at PNAS? Well, if I try to get a paper in their applied mathematics section, I am going to have to get my paper through a statistician. And I have had a paper desk-rejected because the formulation contained in my paper did not constitute a statistical model. And that's true---it didn't. But I submitted an applied mathematics paper---not a statistics paper---and therefore I want to have it judged by card-carrying applied mathematicians. PNAS purports to represent applied mathematics, but it doesn't. There needs to be truth in advertising. They need to either claim that applied mathematics isn't part of their purview (which, by the way, I do not think is the right solution), or their list of editors in "Applied Mathematical Sciences" must include at least one actual applied mathematician!

Note: There is some overlap between models in applied mathematics and statistics when it comes to ensembles of random graphs, but even then applied mathematicians and statisticians tend to look at these beasts in different ways.