Hi all,

suppose I have a dependent variable y_i that I model through a linear regression and one fixed covariate x_i. Now suppose that I have a scale transformation for the y_i in a way that \tilde{y}_i = y_{i} \beta AND \beta has normal distribution with mean \mu_\beta and standard deviation \sigma_\beta. I am wondering if this model is actually identifiable w.r.t. to \beta and the regression coefficient \alpha (see below)?

```
data {
int<lower=1> N;
vector[N] xs;
vector[N] ys;
real mean_alpha;
real mean_beta;
real<lower=0> sd_alpha;
real<lower=0> sd_beta;
}
parameters {
real alpha;
real beta;
real<lower=0> sigma;
}
model {
vector[N] ys_resc;
sigma ~ cauchy(0,3);
alpha ~ normal(mean_alpha, sd_alpha);
beta ~ normal(mean_beta, sd_beta);
ys_resc = ys*beta;
ys_resc ~ normal(alpha*xs,sigma);
}
```