Observed data with uncertainty described by an irregular distribution

If uncertainty was described by an irregular distribution, then it could be, for example, multimodal, and there is no way of putting multimodal into “Y_obs” and describing it in terms of σ and μ.

That being said, you can create multimodal sources of noise via this

You can even try to “clip away” portions from your noise if you suspect there is something weird going on see a nice topic about this:

So you know it is still way flexible beyond just a couple of known distributions to model your noise. I am aware these examples are not solutions to your problem but just emphasizing the point that it is still quite flexible.

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