```
data {
int<lower=0> N;
int<lower=0> K;
matrix[N,K] y;
matrix[N,K] X;
}
parameters {
matrix[K,K] lambda_hat;
matrix[K,K] sigma_0;
matrix[K,K] L;
}
transformed parameters {
matrix[K,N] mu;
vector[4] v;
for (i in 1:K)
v[i]=1;
for (i in 1:N)
mu[,i]=lambda_hat*X[i,]';
}
model {
sigma_0~ inv_wishart(K,diag_matrix(v));
lambda_hat~ wishart(K,diag_matrix(v));
for (t in 1:N)
y[t,]'~ multi_normal(y[(t-1),]'+mu[,t],sigma_0);
}
```

Above is my hierarchical model, then I run the following code,

```
rt = stan(file = "mystancode.stan",data = dataList,iter=2000,warmup=1500,chains = 4,thin=25)
```

Then I am getting the following error,

```
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -1.61381. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -16.0546. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 11.1906. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -1.29482. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -1.612. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 0.623838. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 0.701463. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 0.904612. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -1.10447. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 0.706109. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 3.27242. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 40.5057. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is -1.54971. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: inv_wishart_lpdf: LDLT_Factor of random variable is not positive definite. last conditional variance is 0.638855. (in 'modeld4ca7d2dbf_mystancode' at line 26)
Chain 1:
Chain 1: Initialization between (-2, 2) failed after 100 attempts.
Chain 1: Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
```

Please help me out and let me know what prior should I choose for variance covariance matrix and other things to help me out with this code.