I understand Bayesian look at the quantile. But is it useful to look at the posterior mean and posterior median?

How to explain it in the plain English?

  • $\begingroup$ You have to consider Bayesian decision theory, ie the addition of a loss function to the Bayesian framework. $\endgroup$ – Xi'an Dec 13 '20 at 14:47
  • $\begingroup$ When talking about a distribution, we often use summary statistics, such as mean, median, sd, ... In Bayesian, after observing the data, each parameter has a posterior distribution. From this distribution, any summary has prefix posterior. Therefore, we have terms "posterior mean", ... $\endgroup$ – TrungDung Dec 13 '20 at 20:33
  • $\begingroup$ To know if something is meaningful, we must know what you want to do, your goal. You didn't tell us! $\endgroup$ – kjetil b halvorsen Dec 13 '20 at 20:34

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