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:

- The conclusions are about the model's mechanism, and not about nature's mechanism.

It follows that:

- If the model is a poor emulation of nature, the conclusions may be wrong.