Perform model fit evaluation in Bayesian way when sampling from the custom distribution is not known

Actually the Wald defined in PyMC already has a shift parameter as well, so you shouldn’t need to implement any distribution at all? Just use pm.Censored with pm.Wald

https://www.pymc.io/projects/docs/en/stable/api/distributions/generated/pymc.Wald.html

https://www.pymc.io/projects/docs/en/latest/api/distributions/censored.html