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real lp_pcount_pois(array[] int y, real log_lambda, vector logit_p, int K, int Kmin){
real fac = 1;
real ff = exp(log_lambda) * prod(1 - inv_logit(logit_p));
real N;
real ky;
int numN = K - Kmin;
for (i in 1:numN){
N = K - i + 1;
ky = 1;
for (j in 1:size(y)){
ky *= N / (N - y[j]);
}
fac = 1 + fac * ff * ky / N;
}
return poisson_log_lpmf(Kmin | log_lambda) +
binomial_logit_lpmf(y | Kmin, logit_p) +
log(fac);
}
vector get_loglik_pcount(array[] int y, int M, array[,] int J, array[,] int si, vector log_lambda,
vector logit_p, int z_dist, real beta_scale, int K, array[] int Kmin){
vector[M] out;
for (i in 1:M){
out[i] = lp_pcount_pois(y[si[i,1]:si[i,2]], log_lambda[i],
logit_p[si[i,1]:si[i,2]], K, Kmin[i]);
}
return out;
}
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