I am trying to implement a stan model presented in “Statistical Rethinking” in Section 14.2, pg 438, R code 14.13. I’ve pasted the example code below:

```
model_code <- '
data{
int N;
int nc_num_missing;
vector[N] kcal;
real neocortex[N];
vector[N] logmass;
int nc_missing[N];
}
parameters{
real alpha;
real<lower=0> sigma;
real bN;
real bM;
vector[nc_num_missing] nc_impute;
real mu_nc;
real<lower=0> sigma_nc;
}
model{
vector[N] mu;
vector[N] nc_merged;
alpha ~ normal(0,10);
bN ~ normal(0,10);
bM ~ normal(0,10);
mu_nc ~ normal(0.5,1);
sigma ~ cauchy(0,1);
sigma_nc ~ cauchy(0,1);
// merge missing and observed
for ( i in 1:N ) {
nc_merged[i] <- neocortex[i];
if ( nc_missing[i] > 0 ) nc_merged[i] <- nc_impute[nc_missing[i]];
}
// imputation
nc_merged ~ normal( mu_nc , sigma_nc );
// regression
mu <- alpha + bN*nc_merged + bM*logmass;
kcal ~ normal( mu , sigma );
}'
```

My question specifically pertains to the instantiation of `nc_merged`

and how the prior is assigned. My understanding is that `mc_merged`

is an object which stores data points from `neocortex`

if they exist, and then assigns an entry from `nc_inpute`

to those entries. Thus, my guess is that the next line assigns a prior over the terms in `nc_merged`

which are empty, and does nothing to the entries whose fields are present.

If I were correct, I would assume the following model definition would give identical results:

```
model{
vector[N] mu;
vector[N] nc_merged;
alpha ~ normal(0,10);
bN ~ normal(0,10);
bM ~ normal(0,10);
mu_nc ~ normal(0.5,1);
sigma ~ cauchy(0,1);
sigma_nc ~ cauchy(0,1);
// imputation
nc_impute ~ normal( mu_nc , sigma_nc );
// merge missing and observed
for ( i in 1:N ) {
nc_merged[i] <- neocortex[i];
if ( nc_missing[i] > 0 ) nc_merged[i] <- nc_impute[nc_missing[i]];
}
// regression
mu <- alpha + bN * nc_merged + bM * logmass;
kcal ~ normal( mu , sigma );
}'
```

where I assign a prior to `nc_impute`

before constructing the `nc_merged`

vector. However, the two models give me different inference results, and so I presume I am misunderstanding what the example in Statistical Rethinking is doing.

Any help clarifying this discrepancy would be much appreciated!