Prediction isn’t everything, but everything is prediction – Beragampengetahuan

This is Leo.

Explanation or explanatory modeling can be considered to be the use of statistical models for testing causal hypotheses or associations, e.g. between a set of covariates and a response variable. Prediction or predictive modeling, (supposedly) on the other hand, is the act of using a model—or device, algorithm—to produce values of new, existing, or future observations. A lot has been written about the similarities and differences between explanation and prediction, for example Breiman (2001), Shmueli (2010), Billheimer (2019), and many more.

These are often thought to be separate dimensions of statistics, but Jonah and I have been discussing for a long time that in some sense there may actually be no such thing as explanation without prediction. Basically, although prediction itself is not the only goal of inferential statistics, everything—every objective—in inferential statistics can be reframed through the lense of prediction.

Hypothesis testing, ability estimation, hierarchical modeling, treatment effect estimation, causal inference problems, etc., can all be described in our opinion from a (inferential) predictive perspective. So far we have not found an example for which there is no way to reframe it as prediction problem. So I ask you: is there any inferential statistical ambition that cannot be described in predictive terms?

P.S. Like Billheimer (2019) and others, we think that inferential statistics should be considered as inherently predictive and be focused primarily on probabilistic predictions of observable events and quantities, rather than focusing on statistical estimates of unobersvable parameters that do not exist outside of our highly contrived models. Similarly, we also feel that the goal of Bayesian modeling should not be taught to students as finding the posterior distribution of unobservables, but rather as finding the posterior predictive distribution of the observables (with finding the posterior as an intermediate step); even when we don’t only care about predictive accuracy and we still care about understanding how a model works (model checking, GoF measures), we think the predictive modeling interpretation is generally more intuitive and effective.