Hyperpriors for hierarchical models with Stan

Question

I'm looking to fit a model to estimate multiple probabilities for binomial data with Stan. I was using beta priors for each probability, but I've been reading about using hyperpriors to pool information and encourage shrinkage on the estimates.

I've seen this example to define the hyperprior in pymc, but I'm not sure how to do something similar with Stan

@pymc.stochastic(dtype=np.float64)
def beta_priors(value=[1.0, 1.0]):
    a, b = value
    if a <= 0 or b <= 0:
        return -np.inf
    else:
        return np.log(np.power((a + b), -2.5))

a = beta_priors[0]
b = beta_priors[1]

With a and b then being used as parameters for the beta prior.

Can anybody give me any pointers on how something similar would be done with Stan?

Answer 1

Following suggestions in the comments I'm not sure that I will follow this approach, but for reference I thought I'd at least post the answer to my question of how this could be accomplished in Stan.

After some asking around on Stan Discourses and further investigation I found that the solution was to set a custom density distribution and use the target += syntax. So the equivalent for Stan of the example for pymc would be:

parameters {
  real<lower=0> a;
  real<lower=0> b;
  real<lower=0,upper=1> p;
  ...
}

model {
  target += log((a + b)^-2.5);

  p ~ beta(a,b)
  ...
}