3.1 Missing Data
Stan treats variables declared in the data and
transformed data blocks as known and the variables in the
parameters block as unknown.
An example involving missing normal observation could be coded as follows.10
data {
int<lower=0> N_obs;
int<lower=0> N_mis;
real y_obs[N_obs];
}
parameters {
real mu;
real<lower=0> sigma;
real y_mis[N_mis];
}
model {
y_obs ~ normal(mu, sigma);
y_mis ~ normal(mu, sigma);
}The number of observed and missing data points are coded as data with
non-negative integer variables N_obs and N_mis. The
observed data are provided as an array data variable y_obs.
The missing data are coded as an array parameter, y_mis. The
ordinary parameters being estimated, the location mu and scale
sigma, are also coded as parameters. The model is vectorized
on the observed and missing data; combining them in this case would be
less efficient because the data observations would be promoted and
have needless derivatives calculated.