A full Bayesian analysis requires specifying prior distributions $f(\alpha)$ and
$f(\boldsymbol{\beta})$ for the intercept and vector of regression coefficients.
When using `stan_glm`, these distributions can be set using the 
`prior_intercept` and `prior` arguments. The `stan_glm` function supports a
variety of prior distributions, which are explained in the __rstanarm__
documentation (`help(priors, package = 'rstanarm')`).

As an example, suppose we have $K$ predictors and believe --- prior to seeing 
the data --- that $\alpha, \beta_1, \dots, \beta_K$ are as likely to be positive
as they are to be negative, but are highly unlikely to be far from zero. These
beliefs can be represented by normal distributions with mean zero and a small
scale (standard deviation). To give $\alpha$ and each of the $\beta$s this prior
(with a scale of 1, say), in the call to `stan_glm` we would include the
arguments `prior_intercept = normal(0,1)` and 
`prior = normal(0,1)`.

If, on the other hand, we have less a priori confidence that the parameters will
be close to zero then we could use a larger scale for the normal distribution 
and/or a distribution with heavier tails than the normal like the Student t 
distribution. __Step 1__ in the "How to Use the __rstanarm__ Package" vignette 
discusses one such example.