Prediction, missing data, etc. in Stan

library(rstan)

N <- 1001

N_miss <- ceiling(N / 10)

N_obs <- N - N_miss

mu <- 3

sigma <- 2

y_obs <- rnorm(N_obs, mu, sigma)

missing_data_code <-

'

data {

  int N_obs;

  int N_miss;

  real y_obs[N_obs];

}

parameters {

  real mu;

  real sigma;

  real y_miss[N_miss];

}

model {

  // add prior on mu and sigma here if you want

  y_obs ~ normal(mu,sigma);

  y_miss ~ normal(mu,sigma);

}

generated quantities {

  real y_diff;

  y_diff <- y_miss[101] - y_miss[1];

}

'

results <- stan(model_code = missing_data_code,

                data = list(N_obs = N_obs, N_miss = N_miss, y_obs = y_obs))

y_diff <- apply(extract(results, c("y_miss[1]", "y_miss[101]")), 1:2, diff)