Yes - the most enlightening concept for me was "Highest Probability Density Interval" which basically always is clustered around the mean. But you can choose any interval which contains as much probability mass!
It's a fairly common "mistake" to assume that the MLE is useful as a point estimate and without considering covariance/spread/CI/HPDI/FIM/CRLB/Entropy/MI/KLD or some other measure of precision given the measurement set.
https://en.wikipedia.org/wiki/Credible_interval#Choosing_a_c...
It's a fairly common "mistake" to assume that the MLE is useful as a point estimate and without considering covariance/spread/CI/HPDI/FIM/CRLB/Entropy/MI/KLD or some other measure of precision given the measurement set.