Reading a lot about non-centered parametrisation I am keen to find such version for the student-t distribution when I want to replace normal priors

From Matt’s comment in https://groups.google.com/forum/#!topic/stan-users/EAGOHgnintY

I assume

```
beta ~ student_t(nu, mu, sigma);
nu ~ gamma(2,0.1);
mu ~ normal(0,1);
sigma ~ cauchy(0,2.5);
```

=

```
beta = mu + beta_z * sigma / sqrt(tau);
beta_z ~ normal(0,1);
tau ~ gamma(nu/2, nu/2);
nu ~ gamma(2,0.1);
mu ~ normal(0,1);
sigma ~ cauchy(0,2.5);
```

P.S. Is this a lot different from (?)

```
beta = mu + beta_z * sigma;
beta_z ~ student_t(nu,0,1);
nu ~ gamma(2,0.1);
mu ~ normal(0,1);
sigma ~ cauchy(0,2.5);
```