How to understand how to set prior for Intercepts (e.g. model form y ~ 1 + x)?

Modeling
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How to understand how to set prior for Intercepts (e.g. model form y ~ 1 + x)?

Is the prior for this perhaps predictable from the response’s distribution?

Or should it be left very weak (i.e. one doesn’t have any prior about it, since it’s not one of the predictors).

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Concerning how to choose priors, you could have a look at the Prior distribution vignette from rstanarm.

Concerning how to set priors in brms you should check the set_prior function