Hello,

I might be missing something in the documentation, but I’m trying to understand whether there is an easy way to undertake a regression (`lm`

/`glm`

) where all of my coefficients are subject to a common normal or student-t prior that is adapted as a free parameter.

**Things I have looked at**

From https://mc-stan.org/rstanarm/reference/stan_glm.html:

- One could use eg
`prior=normal()`

or`prior=student_t()`

, but these use fixed-width priors that are not fitted. (Even if the data is re-scaled so that the standard deviation of each column in the design matrix has a standard deviation of 1, this is still true). - One can use the hierarchical shrinkage families
`prior=hs()`

or`prior=hs_plus()`

but these have geometries that are difficult to sample from, and thus can be very slow

**Basically what I’m looking for**

Taking the example from 1.1 Linear regression | Stan User’s Guide and modifying it, I’m really looking for something that does the following, where “THIS LINE NEW” has been added as annotation.

```
data {
int<lower=0> N; // number of data items
int<lower=0> K; // number of predictors
matrix[N, K] x; // predictor matrix
vector[N] y; // outcome vector
}
parameters {
real alpha; // intercept
vector[K] beta; // coefficients for predictors
real<lower=0> sigma_beta; // THIS LINE NEW
real<lower=0> nu_beta; // THIS LINE NEW
real<lower=0> sigma; // error scale
}
model {
beta ~ student_t(nu_beta, 0, sigma_beta); // THIS LINE NEW
y ~ normal(x * beta + alpha, sigma); // likelihood
}
```

Is there a way of easily doing this within `rstanarm`

or `brms`

? Or does this require a custom model like the one shown above?

Thank you!