The following is the R code for using brm_multiple to perform multivariate logistic regression based upon brms package. y is binary variable.

```
fit=brm_multiple(y~age+group_1+group_2+group_3,
data=imp,chains=4,iter=5000,warmup=2500,
prior=c(set_prior('normal(-0.1,0.5)',class='b',coef='group_1'),
set_prior('normal(-0.1,0.5)',class='b',coef='group_2'),
set_prior('normal(-0.1,0.5)',class='b',coef='group_3'),
set_prior('normal(-0.1,0.5)',class='b',coef='age')
)
```

The above model assumes independent priors and does not impose a hyper prior to regularize all coefficients. I want the following model specified.

y\sim Normal(\beta_{age}age+\beta_1group_1+\beta_2group_2+\beta_3group_3+\beta_0,\sigma^2) where (\beta_0,\beta_{age},\beta_1,\beta_2,\beta_3)\sim Normal(\alpha,\Sigma),\alpha\sim Normal((0,0,0,0,0),\Sigma_1) where \Sigma_1 is known,\sigma follows inverse chi square distribution and \Sigma follows inverse Wishart distribution.

This model will regularize all coefficients.