I am fitting two different datasets (y_1 and y_2) that denote two different quantities (counts of cells and proportions of marker+ cells viz.), which are iid observations.

Both these quantities can be derived from the same model (M) with shared parameters, such that

How to specify this optimally in stan? How does stan handle this? Does it form a joint distribution of y_1 and y_2 while fitting the model M(\theta) simultaneously on them? Here, \theta is an array of \alpha, \beta, \text{ and } \delta.

The general practice I came across to specify this model in stan is,

```
model{
alpha ~ normal(0.3, 0.2);
beta ~ normal(0.01, 0.2);
delta ~ normal(0.03, 0.2);
sigma1 ~ cauchy(0, 1);
sigma2 ~ cauchy(0, 1);
y1 ~ normal(mu1, sigma1);
y2 ~ normal(mu2, sigma2);
}
```

where \mu_1 and \mu_2 are defined in the transformed parameters block.

Is this right?