Modeling for Understanding v. Modeling for Numbers
I draw a distinction between Modeling for Numbers, which aims to address how much, when, and where questions, and Modeling for Understanding, which aims to address how and why questions. For-numbers models are often empirical, which can be more accurate than their mechanistic analogues as long as they are well calibrated and predictions are made within the domain of the calibration data. To extrapolate beyond the domain of available system-level data, for-numbers models should be mechanistic, relying on the ability to calibrate to the system components even if it is not possible to calibrate to the system itself. However, development of a mechanistic model that is reliable depends on an adequate understanding of the system. This understanding is best advanced using a for-understanding modeling approach. To address how and why questions, for-understanding models have to be mechanistic. The best of these for-understanding models are focused on specific questions, stripped of extraneous detail, and elegantly simple. Once the mechanisms are well understood, one can then decide if the benefits of incorporating the mechanism in a for-numbers model is worth the added complexity and the uncertainty associated with estimating the additional model parameters.
Key wordsmodeling prediction theory mechanistic empirical extrapolation interpolation
This work has been supported in part by NSF grants 0949420, 1026843, 1065587, 1107707, and 1503781. I also thank Gus Shaver, Göran Ågren, Bonnie Kwiatkowski, and Joe Vallino for many years of batting around these ideas.
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