Multiple-output Gaussian process fitting error

Modeling
1

Whoever has time to read this,

I am getting an error when tying to parse a multiple-output Gaussian process model with predictive inference. I am a beginner in using Stan and my code is mainly based on the Stan’s User Guide. My model is as follows:

data {
  int<lower=1> N1;
  int<lower=1> D;
  int<lower=1> q;
  int<lower=1> Np;
  matrix[N1, q] x1;
  matrix[N1, D] y;
  matrix[Np, q] xp;
}
transformed data {
  real delta = 1e-9;
  int<lower=1> N = N1 + Np;
  matrix[N,q] X;
  for (i in 1:N1) X[i,] = x1[i,];
  for (i in 1:Np) X[N1 + i,] = xp[i,];
}

parameters {
  vector<lower=0>[q-1] theta;
  vector[q] beta;
  vector<lower=0>[D] alpha;
  cholesky_factor_corr[D] L_Omega;
  matrix[N, D] eta;
}

transformed parameters{
    real<lower=0> sigma;
    matrix[N, D] f;
    matrix[N,q-1] z;
    vector[N] mu = X * beta;
    matrix[N,D] MEAN = append_col(mu,mu);
  
  for(i in 2:q)
  z[,i-1] = X[, i]/theta[i-1];

  {
    matrix[N, N] L_K;
    matrix[N, N] K;
    
    for (i in 1:(N - 1)) {
    K[i, i] = 1 + delta;
    for (j in (i + 1):N) {
      K[i, j] = exp(-sum(square(z[i, ] - z[j, ])));
      K[j, i] = K[i, j];
    }
  }
  K[N, N] = 1 + delta;
    
   // matrix[N, N] K = cov_exp_quad(x, 1.0, rho);
   // diagonal elements
   // for (n in 1:N)
    //  K[n, n] = K[n, n] + delta;

    L_K = cholesky_decompose(K);
    f = MEAN + L_K * eta
        * diag_pre_multiply(alpha, L_Omega)';
  }
  
}
model {
  for(i in 1:(q-1))
  theta[i] ~ exponential(0.2);
  beta[1] ~ normal(0,10);
  for(i in 2:q)
  beta[i] ~ normal(0,4);
  
  alpha ~ std_normal();
  sigma ~ std_normal();
  L_Omega ~ lkj_corr_cholesky(3);
  to_vector(eta) ~ std_normal();

  to_vector(y) ~ normal(to_vector(f[1:N1,]), sigma);
}
generated quantities {
  matrix[D, D] Omega;
  matrix[Np, D] yp;
  Omega = L_Omega * L_Omega';
  to_vector(yp) = normal_rng(to_vector(f[(N1+1):N]), sigma);// something's wrong here

}

The errors I get are:

Left-hand side of sampling statement (~) may contain a non-linear transform of a parameter or local variable.
If it does, you need to include a target += statement with the log absolute determinant of the Jacobian of the transform.
Left-hand-side of sampling statement:
sigma ~ std_normal(…)
Illegal statement beginning with non-void expression parsed as
to_vector(yp)
Not a legal assignment, sampling, or function statement. Note that

  • Assignment statements only allow variables (with optional indexes) on the left;
  • Sampling statements allow arbitrary value-denoting expressions on the left.
  • Functions used as statements must be declared to have void returns

error in ‘model151022a7486e_MVARgpe’ at line 79, column 2

77:   Omega = L_Omega * L_Omega';
78:   //to_vector(yp) = normal_rng(to_vector(f[((N1+1):N),]), sigma);
79:   to_vector(yp) = normal_rng(to_vector(f[(N1+1):N]), sigma);
     ^
80:   //for (i in 1:Np)

PARSER EXPECTED: <one of the following:
a variable declaration, beginning with type
(int, real, vector, row_vector, matrix, unit_vector,
simplex, ordered, positive_ordered,
corr_matrix, cov_matrix,
cholesky_corr, cholesky_cov
or a
or ‘}’ to close variable declarations and definitions>
Error in stanc(file = file, model_code = model_code, model_name = model_name, :
failed to parse Stan model ‘MVARgpe’ due to the above error.

Thanks!

2

Loop over N1 and D

for (n in 1:N1) {
    for (d in 1:D) {
        yp[n, d] = normal_rng(f [N1 + n, d], sigma);
      }
}
4

Thanks very much. It now begins to parse, but generates the following error:

DIAGNOSTIC(S) FROM PARSER:
Info:
Left-hand side of sampling statement (~) may contain a non-linear transform of a parameter or local variable.
If it does, you need to include a target += statement with the log absolute determinant of the Jacobian of the transform.
Left-hand-side of sampling statement:
sigma ~ std_normal(…)

[1] “Error in sampler$call_sampler(args_list[[i]]) : Initialization failed.” “In addition: Warning message:”
[3] “In system(paste(CXX, ARGS), ignore.stdout = TRUE, ignore.stderr = TRUE) :” " ‘C:/rtools40/usr/mingw_/bin/g++’ not found"
[1] “error occurred during calling the sampler; sampling not done”