Distance modeling for point transect data, translated from Sec. 8.3.4 of "Applied Hierarchical Modeling in Ecology, vol. 1"

distance_sampling-3.stan

data {
  int<lower = 1> N_D;
  int<lower = 1> N_ind;
  real B;
  int <lower = 1, upper = N_D>  D_class[N_ind];
  real<lower = 0, upper = B> Delta;           // Width of distance bins
  vector<lower = 0, upper = B>[N_D] Midpt;    // Interval mid-points
}
transformed data {
  vector<lower = 0, upper = 1>[N_D] pi = 2 * Midpt / square(B) * Delta;
}
parameters {
  real<lower = 0> sigma;
}
transformed parameters {
  vector<lower = 0, upper = 1>[N_D] p = exp(-(Midpt .* Midpt)
                                            / (2 * square(sigma)));
  vector<lower = 0, upper = 1>[N_D] f = p .* pi;
  real pcap = sum(f);
  simplex[N_D] fc = f / pcap;
}
model {
  sigma ~ normal(0, 10);
  D_class ~ categorical(fc);
}
generated quantities {
 real N = N_ind / pcap;
 real D = N / (pi() * square(B));
}