Hello, everyone. I have a problem that X,Y \sim N(\mu,\Sigma), where the TRUE value is that \mu=(10,20) and \Sigma=(\begin{matrix}10&4\\4&30\end{matrix}).

I KNOW how to estimate with stan-defined functions and now i want to practice in user-defined functions. Now here is my stan code:

```
code='
functions{
real fun_log(vector X,vector Y,real mu1,real mu2,real sigma1, real sigma2, real rho){
vector [num_elements(X)] prob;
real lprob;
for (i in 1:num_elements(X)){
##Likelihood function
prob[i] <- (2*pi()*sigma1*sigma2*sqrt(1-rho^2))^(-1)*exp(-1/2/(1-rho^2)*((X[i]-mu1)^2/sigma1^-2*rho*(X[i]-mu1)*(Y[i]-mu2)/sigma1/sigma2+(Y[i]-mu2)^2/sigma2^2));
}
lprob <- sum(log(prob));
return lprob;
}
}
data{
int N;
vector[N] X;
vector[N] Y;
}
parameters{
real<lower=0> rho;
real<lower=0> sigma1;
real<lower=0> sigma2;
real mu1;
real mu2;
}
model{
append_row(X,Y)~fun(rho,sigma1,sigma2,mu1,mu2);
}
'
```

But it says that

```
Unknown variable: append_row
No matches for:
vector ~ fun(real, real, real, real, real)
```

Can some one help me to debug the model? Thanks!