# What's wrong with my stan code for estimating parameters with multivariate distribution

**URL:** <https://discourse.mc-stan.org/t/whats-wrong-with-my-stan-code-for-estimating-parameters-with-multivariate-distribution/9997>\
**Category:** Modeling\
**Created:** [July 31, 2019, 12:08pm UTC](https://discourse.mc-stan.org/t/whats-wrong-with-my-stan-code-for-estimating-parameters-with-multivariate-distribution/9997 "2019-07-31T12:08:44Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Keydom\_Zhang](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/keydom_zhang/32/5152_2.png) [@Keydom\_Zhang](https://discourse.mc-stan.org/u/Keydom_Zhang)\
**Post date:** [July 31, 2019, 12:08pm UTC](https://discourse.mc-stan.org/t/whats-wrong-with-my-stan-code-for-estimating-parameters-with-multivariate-distribution/9997/1 "2019-07-31T12:08:44Z")

</div>

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:

```stan
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!

---

<div class="post-metadata">

**Author:** ![erognli](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/erognli/32/5181_2.png) [@erognli](https://discourse.mc-stan.org/u/erognli)\
**Post date:** [July 31, 2019, 12:19pm UTC](https://discourse.mc-stan.org/t/whats-wrong-with-my-stan-code-for-estimating-parameters-with-multivariate-distribution/9997/2 "2019-07-31T12:19:12Z")

</div>

Judging from the error message, maybe you need to declare a local variable for the return value of append\_row, and have this as the target of your sampling statement?

Also, your return from the function is a single real, so it won’t accept a vector as target?

---

<div class="post-metadata">

**Author:** ![jjramsey](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jjramsey/32/3319_2.png) [@jjramsey](https://discourse.mc-stan.org/u/jjramsey)\
**Post date:** [July 31, 2019, 12:51pm UTC](https://discourse.mc-stan.org/t/whats-wrong-with-my-stan-code-for-estimating-parameters-with-multivariate-distribution/9997/3 "2019-07-31T12:51:22Z")

</div>

I’m pretty sure that the problem is that `fun_log` is defined incorrectly. In a log-probability function, all arguments except the first are the parameters to the function. Here, `Y` is treated as a parameter, so it belongs on the right-hand side of the “`~`” operator, as part of the arguments to `fun`. In short, given how you defined `fun_log`, the corresponding sampling statement _has_ to be

```stan
X ~ fun(Y, rho,sigma1,sigma2,mu1,mu2);

```

What you probably really want to do is define `fun_log` like this:

```stan
real fun_log(matrix XY, real mu1,real mu2,real sigma1, real sigma2, real rho){
    vector [cols(XY)] prob;
    real lprob;
    for (i in 1:cols(XY)){
     ##Likelihood function
      prob[i] <- (2*pi()*sigma1*sigma2*sqrt(1-rho^2))^(-1)*exp(-1/2/(1-rho^2)*((XY[1,i]-mu1)^2/sigma1^-2*rho*(XY[1,i]-mu1)*(XY[2,i]-mu2)/sigma1/sigma2+(XY[2,i]-mu2)^2/sigma2^2));
    }
    lprob <- sum(log(prob));
    return lprob;
    }

```

Then define the `data` block as follows:

```stan
data{
  int N;
  matrix[2, N] XY;
}

```

The sampling statement in your model would then be

```stan
XY ~ fun(rho,sigma1,sigma2,mu1,mu2);

```