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//Removal sampling
//p can be any length > 1
vector pi_removal(vector p){
int J = num_elements(p);
vector[J] pi_out;
pi_out[1] = p[1];
for (j in 2:J){
pi_out[j] = pi_out[j-1] / p[j-1] * (1-p[j-1]) * p[j];
}
return pi_out;
}
//Double observer
//p must have 2 elements
vector pi_double(vector p){
vector[3] pi_out;
pi_out[1] = p[1] * (1 - p[2]);
pi_out[2] = p[2] * (1 - p[1]);
pi_out[3] = p[1] * p[2];
return pi_out;
}
vector pi_fun(int pi_type, vector p, int J){
vector[J] out;
if(pi_type == 0){
out = pi_double(p);
} else if(pi_type == 1){
out = pi_removal(p);
} else {
reject("Invalid pi function type");
}
return out;
}
real lp_multinomPois(int[] y, real log_lambda, vector logit_p, int pi_type){
real loglik = 0.0;
real lam = exp(log_lambda);
int J = num_elements(y);
int np = num_elements(logit_p);
vector[np] p;
vector[J] cp;
for (i in 1:np){
p[i] = inv_logit(logit_p[i]);
}
cp = pi_fun(pi_type, p, J);
for (j in 1:J){
loglik += poisson_lpmf(y[j] | lam * cp[j]);
}
return loglik;
}
vector get_loglik_multinomPois(int[] y, int M, int[,] si, vector log_lambda,
vector logit_p, int pi_type){
vector[M] out;
int J = num_elements(logit_p) / M; // use %/% in future version of stan
int pstart = 1;
int pend;
for (i in 1:M){
pend = pstart + J - 1;
out[i] = lp_multinomPois(y[si[i,1]:si[i,2]], log_lambda[i],
logit_p[pstart:pend], pi_type);
pstart += J;
}
return out;
}
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