MMP.7:2 - Problem

The distribution of a subject property and the distribution of its records can differ. Selection changes which cases appear. Coarsening combines several possible values into one report. A common influence makes observations dependent. These transformations remain part of the inference even when a dataset presents every row in the same format.

A formula such as independent errors around a predicted value already makes choices about those transformations. If the choices are left implicit, more data and more accurate computation can reinforce a mistaken interpretation.

The difficulty is to construct the law of the observations from the modeled subject and its recording procedure, preserving the dependencies that matter to the question.