Interesting case. I can see the intuitive case for the median.
I think the mean is more appropriate—in this case, what this is telling you is that your uncertainty is dominated by the possibility of a fat tail, and the priority is ruling it out.
I’d still report both for completeness sake, and to illustrate the low resilience of the guess.
Thanks for the feedback! I am still standing by the median, but it would be nice to empirically investigate similar cases, and see which method performs better!
Interesting case. I can see the intuitive case for the median.
I think the mean is more appropriate—in this case, what this is telling you is that your uncertainty is dominated by the possibility of a fat tail, and the priority is ruling it out.
I’d still report both for completeness sake, and to illustrate the low resilience of the guess.
Very much enjoyed the posts btw
Thanks for the feedback! I am still standing by the median, but it would be nice to empirically investigate similar cases, and see which method performs better!
(I think it seems in principle promising to try to setup toy models of tail prediction, but I’m unsure what the right toy model is here.)