Great discussion here,
Generally speaking there’s a couple of strategies
- Remove or “correct” the data manually
- Use a restrictive prior to discount
- Use a flexible likelihood to accommodate
I write about this in a chapter of my book
https://bayesiancomputationbook.com/markdown/chp_09.html
I also will be giving a PyMCon talk that will include this based off of my experience at SpaceX where this occurred frequently! Stay tuned for that one