Thank you @simon_o for the comment!
Taking the mean is not useful: I’m generating temporal traces from Fourier Series components, so (temporal) averaging will lead to amplitude loss (as in interference). Hence, reconstructions from averages will be wrong. I actually want to see variable traces, not the variability. Thinking about it, the MAP value would also be only a particular value, so maybe it is not better than the mean.
However, the mean of a distribution can be rather meaningless, if the distribution is skewed (possible in my case). So the peak of the density curve would be much better. So I think find_MAP might still be useful, keeping in mind that it might fail on multimodal cases (not the case for me).
I can imagine @twiecki mentioned find_MAP deprecation in the context of NUTS initialization? that’s where I read it. It may be useful with other samplers or, as here, for prediction. If it is only there for historical reasons, wouldn’t it be good to throw a warning?
How about the relation to epsilon? If I take the MAP, is the variability I see only from the model, and does it also come from the data if I pass a trace? Quite confusing, still.