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?
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?