rstanarm: mean vs. median

Machine Learning and Modeling
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stan_lmer prints out its summary giving the means and sd for the parameters rather than medians and mads as may be more frequent in Bayesian analysis. The documentation notes that the printed sds are estimated from the mads to produce a "robust" estimate of the sd. I assume that this print out is designed to look as much as possible like the output of lme4::lmer to reassure frequentists using a Bayesian procedure. But as discussed by CDEager at https://github.com/stan-dev/rstanarm/issues/189, there is some inconsistency in mixing means and medians. (While a weighted mean of subset means is a mean of the whole set, a median of subset medians is not necessarily a median of the whole set.) Of course, since the entire set of draws is available following run of stan_lmer, it is pretty trivial to obtain either means/sds or medians/mads of whatever one wants. Is there a strong argument for preference for median/mad over mean/sd in Bayesian analyses? Would it be better simply to use the set of draws to compute exactly what I want?
Thanks in advance for any comments/discussion by Bayesians that are more experienced than I.
Larry Hunsicker

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I think you do see medians often when viewing statistics regarding how sufficiently the sample space was explored and this should be expected to be analogous to the posterior. I'm almost guaranteed to be less experienced than you, however, to me it doesn't seem reasonable to care about how often a sample is compared other than the degree to which it helps inform a valid representation of the observation.

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If discussion here is slow, you might also try posting a version of this question at Cross Validated (but be sure to follow their posting guidelines!).

Not sure if this discussion gets at what you're asking, but it certainly has plenty of Bayesians talking about dispersion statistics:

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Thanks, jcblum. Mostly well over my head! Fortunately I am not (I think) dealing with a contaminated data set. But thanks for the reference. The discussion is quite interesting and informative. I'll need some time to digest it.

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