I just want to double check (and I hope I’m not being presumptuous here):
You have recently asked a lot of questions about setting discrete priors (e.g. negative binomial, poisson, discrete factor variables in general). I just want to make sure that you aren’t confusing discrete parameters (which do not work in Stan and need to be marginalized out) with discrete covariates (which work just fine in Stan). In the intercept + gender_male model, for example, gender_male is a discrete covariate. In a regression context, gender_male then gets multiplied by a coefficient that gets estimated from the data. This parameter (i.e. the coefficient) is not discrete; it is continuous. It can take any value. You would encode prior information about this coefficient using some appropriate continuous distribution like a Gaussian or a Student t.
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