Stan pointed me to a short article “Why Model?” by J. M. Epstein. The default principle, both in statistics and in machine learning, is to predict. Any act of statistical fitting that involves likelihood is inherently predictive in its nature.
Visualization is in no way different from predictive modeling – it’s just that the (sometimes implicit) model is transparent and interpretable. Visualization is not the only type of interpretable model: even a table with regression coefficients is interpretable, a decision tree is an interpretable model, a list of typical cases is an interpretable model. A 2D scatter plot that nicely shows the difference in outcomes is a model, because the two dimensions used by the plot indeed help distinguish the outcomes.
Most priors are grounded purely in the desire to capture the truth, as such they are predictive priors. But the interpretable models involve priors that are not grounded in prediction – but rather in the human cost of interpretation. The more difficult it is to interpret a parameter, the lower prior probability of interpretation it should have.
In summary, while most mathematical treatment of statistical modeling tends to be focused purely on prediction, there is a good reason why the cost of interpretation should be considered. Epstein’s list of why interpretability matters should motivate us to care:
1. Explain (very distinct from predict)
2. Guide data collection
3. Illuminate core dynamics
4. Suggest dynamical analogies
5. Discover new questions
6. Promote a scientific habit of mind
7. Bound (bracket) outcomes to plausible ranges
8. Illuminate core uncertainties.
9. Offer crisis options in near-real time
10. Demonstrate tradeoffs / suggest efficiencies
11. Challenge the robustness of prevailing theory through perturbations
12. Expose prevailing wisdom as incompatible with available data
13. Train practitioners
14. Discipline the policy dialogue
15. Educate the general public
16. Reveal the apparently simple (complex) to be complex (simple)
[Link to paper corrected. Thanks to Lee Sigelman for pointing it out.]