What is a spatio-temporal model good for?: Validity as a function of purpose and the questions answered by a model

Abstract

The concept of validity is a cornerstone of science. Given this central role, it is somewhat surprising to find that validity remains a rather obscure concept. Unfortunately, the term is often reduced to a matter of ground truth data, seemingly because we fail to come to grips with it. In this paper, instead, we take a purpose-based approach to the validity of spatio-temporal models. We argue that a model application is valid only if the model delivers an answer to a particular spatio-temporal question specifying some experiment including spatio-temporal controls and measures. Such questions constitute the information purposes of models, forming an intermediate layer in a pragmatic knowledge pyramid with corresponding levels of validity. We introduce a corresponding question-based grammar that allows us to formally distinguish among contemporary inference, prediction, retrodiction, projection, and retrojection models. We apply the grammar to corresponding examples and discuss the possibilities for validating such models as a means to a given end.