In Bayesian statistics, we may want to determine at what interval for example 95% of the posterior probability exists. For this we may want to use the Highest Posterior Density Interval (HPDI) which is [1]:
The HPDI is the narrowest interval containing the specified probability mass. If you think about it, there must be an infinite number of posterior intervals with the same mass. But if you want an interval that best represents the parameter values most consistent with the data, then you want the densest of these intervals. That’s what the HPDI is.
Or the Percentile Intervals (PI) [1]:
Intervals of this sort, which assign equal probability mass to each tail, are very common in the scientific literature.
Richard McElreath mentions that HPDI has some advantages over PI, but HPDI is more computationally intensive than PI and suffers from greater simulation variance. So both have their advantages and disadvantages. But PI mainly works well if the distribution isn't too asymmetrical, which in practice is most of the time the case, right?
So I was wondering if anyone could explain and show in what situation you would prefer to use PI
over HPDI
when computational intensity doesn't matter?
Reference:
- Statistical Rethinking, Richard McElreath [1]