I have $N$ methods that each report a posterior probability density for the measurement of $X$.
When $N=2$ and the posteriors are both approximately Gaussian, one can check whether the posteriors agree by comparing their means divided by their standard deviations. This can reveal for example whether the two measurements are more than, say, $5\sigma$ apart and hence significantly different.
What can be analogously done when $N\geq 2$ and/or any of the distributions are not approximately Gaussian?
If the general case is difficult, in the special case where one of the distributions is non-normally distributed but the rest are normally distributed, is there something that can be done there?