Prior on unit norm vectors

General
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1

I am aware that the unit vector type has some potential limitations in practice, nonetheless I would like to try it just to gauge some hypothesis I have. From the documentation thought it is unclear what type of prior I am allowed to specify for it. I haven’t understood if Stan defines a standard prior for it, and hence we should not define it by ourselves, or if wee can define any prior we want and then STAN will try to deal with the normalization under the hood.

An example would be to understand if such a specification makes sense:

......
parameters {
   unit_vector[N] nu_norm[K];
}
....
model{
    for (k in 1:K){
        target += normal_lpdf(nu_norm[k]| 0, sigmap);
.....
}
2

Stan doesn’t require normalization, either explicitly or under the hood, to perform sampling (as long as you don’t intend to work with Bayes factors). You can define any prior density function you wish, and what you will get out is inference based on a prior proportional to your explicit prior truncated by the constraints of the parameter type (unit vector in this case). Note that in general this truncation means that the realized prior margins won’t correspond to the margins of the density function you use explicitly (unless your density function already respects the constraint; i.e. evaluates to zero–negative infinity on the log scale–everywhere the constraint isn’t satisfied).