Statistical vs Mathematical Modeling

Interesting comments,  having been involved in 'mathematical modeling' for a long time ...  it, like statistics has to be evaluated with terms like significance.    Had to be done then, and also needs to be done now.  Math modeling is, as much as statistics, also a discipline.

A short comment on statistical versus mathematical modelling
Andrea Saltelli
Nature Communications volume 10, Article number: 3870 (2019)

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.

While statistical and mathematical modelling share important features, they don’t seem to share the same sense of crisis. Statisticians appear mired in an academic and mediatic debate where even the concept of significance appears challenged, while more sedate tones prevail in the various communities of mathematical modelling. This is perhaps because, unlike statistics, mathematical modelling is not a discipline. It cannot discuss possible fixes in disciplinary fora under the supervision of recognised leaders. It cannot issue authoritative statements of concern from relevant institutions such as e.g., the American Statistical Association or the columns of Nature.

Additionally the practice of modelling is spread among different fields, each characterised by its own quality assurance procedures (see1 for references and discussion). Finally, being the coalface of research, statistics is often blamed for the larger reproducibility crisis affecting scientific production2.

Yet if statistics is coming to terms with methodological abuse and wicked incentives, it appears legitimate to ask if something of the sort might be happening in the multiverse of mathematical modelling. A recent work in this journal reviews common critiques of modelling practices, and suggests—for model validation, to complement a data-driven with a participatory-based approach, thus tackling the dichotomy of model representativeness—model usefulness3. We offer here a commentary which takes statistics as a point of departure and comparison.  .... "