camel2.stan

/*
 * Camel: Multivariate normal with structured missing data 
 * http://www.openbugs.net/Examples/Camel.html
 *
 * integrate out the missing data
 */
transformed data {
  array[4] vector[2] Y;
  array[4] real Y1; // missing y2 
  array[4] real Y2; // msising y1
  
  vector[2] mu;
  matrix[2, 2] S;
  
  mu[1] = 0;
  mu[2] = 0;
  S[1, 1] = 1000;
  S[1, 2] = 0;
  S[2, 1] = 0;
  S[2, 2] = 1000;
  
  Y[1, 1] = 1.;
  Y[1, 2] = 1.;
  Y[2, 1] = 1.;
  Y[2, 2] = -1.;
  Y[3, 1] = -1.;
  Y[3, 2] = 1.;
  Y[4, 1] = -1.;
  Y[4, 2] = -1.;
  
  Y1[1] = 2.;
  Y1[2] = 2.;
  Y1[3] = -2.;
  Y1[4] = -2.;
  
  Y2[1] = 2.;
  Y2[2] = 2.;
  Y2[3] = -2.;
  Y2[4] = -2.;
}
parameters {
  cov_matrix[2] Sigma;
}
transformed parameters {
  real<lower=-1, upper=1> rho;
  rho = Sigma[1, 2] / sqrt(Sigma[1, 1] * Sigma[2, 2]);
}
model {
  for (n in 1 : 4) {
    Y[n] ~ multi_normal(mu, Sigma);
  }
  Y1 ~ normal(0, sqrt(Sigma[1, 1]));
  Y2 ~ normal(0, sqrt(Sigma[2, 2]));
  target += -1.5 * log(determinant(Sigma));
}