Upon my return, I started reading the Annals of Statistics, the flagship journal of theoretical statistics, and was bemused. Every article started with
Assume that the data are generated by the following model: …
followed by mathematics exploring inference, hypothesis testing and asymptotics. There is a wide spectrum of opinion regarding the usefulness of the theory published in the Annals of Statistics to the field of statistics as a science that deals with data. I am at the very low end of the spectrum. Still, there have been some gems that have combined nice theory and significant applications. An example is wavelet theory. Even in applications, data models are universal. For instance, in the Journal of the American Statistical Association (JASA), virtually every article contains a statement of the form:
Assume that the data are generated by the following model: …
I am deeply troubled by the current and past use of data models in applications, where quantitative conclusions are drawn and perhaps policy decisions made.
Statisticians in applied research consider data modeling as the template for statistical analysis: Faced with an applied problem, think of a data model. This enterprise has at its heart the belief that a statistician, by imagination and by looking at the data, can invent a reasonably good parametric class of models for a complex mechanism devised by nature. Then parameters are estimated and conclusions are drawn. But when a model is fit to data to draw quantitative conclusions:
It follows that: