Models and statistical data

Functional models are theoretical constructs. They do not entail anything about the facts of the empirical world, nor are they rendered false by any facts. But reference to the empirical world is indispensable if a model is to be used for (retrospective) explanations or (prospective) predictions; and being interested in quantitative statements the model’s deterministic or stochastic functions need numerical specification. There are thus often reasons to use statistical data to calculate estimates of the functions of a model.