If you are new to continuous predictions then you should focus on the 50% Interval as it gives you most information about your calibration, If you are skilled and use for example a t-distribution then you have σ for the trunk and ν for the tail, even then few predictions should land in the tails, so most data should provide more information about how to adjust σ, than how to adjust ν
Hot take: I think the focus 95% is an artifact of us focusing on p<0.05 in frequentest statistics.
I agree with both points
If you are new to continuous predictions then you should focus on the 50% Interval as it gives you most information about your calibration, If you are skilled and use for example a t-distribution then you have σ for the trunk and ν for the tail, even then few predictions should land in the tails, so most data should provide more information about how to adjust σ, than how to adjust ν
Hot take: I think the focus 95% is an artifact of us focusing on p<0.05 in frequentest statistics.