I hope this question is not too trivial, however since I was not able to find a definitive answer I would like to ask it here.

I found that systematical errors are supposed to be treated as a nuisance prior in a fully bayesian approach, however I am unsure how to implement such a nuisance prior in a model.

In case I am terrible at explaining the question, I hope this clarifies the issue.

I am wondering how to implement a respective nuisance prior in a model similar to the following:

```
model = """
data {
int<lower=0> N; // number of datapoints
vector[N] x; // measured x-value
vector[N] y; // measured y-value
real<lower=0> sigma_stat[N]; // statistical y-error
real<lower=0> sigma_syst[N]; // systematical y-error
}
parameters {
real alpha; // a in the linear model ax+b
real beta; // b in the linear model ax+b
}
model {
// priors
alpha ~ normal(0, 1);
beta ~ normal(0, 1);
// likelihood
y ~ normal(alpha * x + b, sigma_stat);
}
"""
```