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Are these based on a parametric estimate of the distribution, where the parameter samples are aggregated with an average? My overall takeaway from the toy examples (which exhibit skewness and/or multiple modes) is that, with averaging techniques such as mean, the resulting aggregated posterior is a poor representation of the true posterior. However, I have questions about whether such comparisons are fair, since (at least in the case of a known bimodal distribution) averaging techniques are clearly a poor choice. Therefore it feels that the comparison is a bit unfair.