Double beta binomial

Modeling
1

Dear all
I’m trying to model data with a binomial broadened by a mixture of two beta distributions.

Using the stan code below, I get an error Exception: beta_lpdf: Random variable is nan, but must not be nan! which I believe means that I need to constrain theta. I have not been able to do this with a prior. Is there another way?

Thanks
Alex

data {
    int N;
    int n[N];
    int y[N];
}
parameters {
  real<lower=0, upper=1> lambda;
  real<lower=0, upper=1> mu1;
  real<lower=0, upper=1> rho1;
  real<lower=0, upper=1> mu2;
  real<lower=0, upper=1> rho2;
}
model {
  real theta;
  lambda ~ beta(5,5);
  mu1 ~ beta(500, 500);
  rho1 ~ exponential(1000);
  mu2 ~ beta(5, 5);
  rho2 ~ exponential(10);
  target += log_mix(
      lambda, 
      beta_lpdf(theta | mu1 * (1 - rho1)/rho1, (1 - mu1) * (1 - rho1)/rho1),
      beta_lpdf(theta | mu2 * (1 - rho2)/rho2, (1 - mu2) * (1 - rho2)/rho2));
  target += binomial_lpmf(y | n, theta);
}
2

theta needs to be declared in the parameters block as

real<lower=0, upper=1> theta;