[m-murphy]

Agreed! I also think it's extremely important as practitioners to know what we're even trying to estimate. Expected value (i.e. least squares regression) is the usual first thing to go for, does that even matter? We're probably actually interested in something like an upper quantile for planning purposes. And then the whole model component of it, the interval that's being simultaneously estimated is model driven and if that's wrong, then the interval is meaningless. There's a lot of space for super interesting and impactful work in this area IMO, once you (the practitioner) think more critically about the objective. And then don't even get me started on interventions and causal inference...

[borroka]

From a statistical point of view, I agree that there is a lot of interesting and impactful work to be done on estimating predictive intervals, more in ML than in traditional statistical modeling.

I have more doubts when it comes to actions taken when considering properly estimated predictive intervals. Even I, who have a good knowledge of statistical modeling, after hearing "the median survival time for this disease is 5 years," do not stop to think that the median is calculated/estimated on an empirical distribution, so there are people who presumably die after 2 years, others after 8. Well, that depends on the variance.

But if I am so strongly drawn to a central estimate, is there any chance for others not so used to thinking about distributions?

[fjkdlsjflkds]

> We're probably actually interested in something like an upper quantile for planning purposes.

True. But a conditional quantile is much harder to accurately estimate from data than a conditional expectation (particularly if you are talking about extreme quantiles).

[m-murphy]

Oh absolutely, so it's all the more important to be precise in what we're estimating and for what purpose, and to be honest about our ability to estimate it with appropriate uncertainty quantification (such as by using conformal prediction methods/bootstrapping).