Sorry, I was unclear! What I mean is that the type of sampling distribution the data comes from can be integrated as part of the prior information, in most cases. It is obviously an essential component of the model. The point was in trying to attenuate the criticism that reference priors, like Jeffreys’, are contradicting the Likelihood Principle… The prior distribution is also impacted by the model, as the parameter very rarely exists w/o the model. I hope this is clearer!

]]>I’m political scientist, so I don’t trust that much on my statistical knowledge, but I thought that, since the likelihood is our model to the data (I usually think as my model to the data generator process), why the shape of the sampling distribution is not part of the likelihood?

I mean, if I have some vector y and some matrix of covariates X, and I assume my data are exchangeable and I’m assuming there is no sampling bias etc. my assumptions of the sampling process should be reflected in my model.

I don’t know if I made myself clear… If not, please just ask for clarification…

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