I completely agree with cluhmann’s answer. I would just add that the posterior mode for continuous variables doesn’t really correspond to any choice of loss function (see passage after “When the loss function is of the form…” here Maximum a posteriori estimation - Wikipedia). In addition, find_MAP can have issues with hierarchical models. So I would suggest steering away from that. To choose from the others, you can take a look at cluhmann’s resources. The posterior mean, for example, minimises the mean square error loss and can be reasonable choice in many cases.
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