I have a rather non-normal marginalized posterior for some parameters, resulting from a Bayesian MCMC. Example:
I know that the actual distribution is what truly represents the parameter, but I need to report a point estimate. In such a case, I believe the mode would be better than the mean or median, but I'm not sure how to justify this other than saying "the mode looks like a more reasonable point estimate for the parameter".
Is there a more "statistical" justification for selecting either point estimate?