# Getting multivariate Gaussian prior working in a bayesian logistic regression model

Hi all!

I have a Bayesian Logistic Regression Model that runs with univariate Gaussian priors on each element of the parameter vector \beta.

data {
int<lower = 1> N;
int K;
matrix[N,K] x;
int<lower = 0, upper = 1> y[N];
}
parameters {
vector[K] beta;
}
model {
y ~ bernoulli_logit(x*beta);
beta ~ normal(0, 3);
}


However, I am having difficult converting the prior over the parameter vector \beta to a multivariate Gaussian with a specified mean and covariance matrix.

Here is what I have so far (but it does not work)

data {
int<lower = 0> N;
int K;
matrix[N,K] x;
int<lower = 0, upper = 1> y[N];
vector[K] prior_mean;
matrix[K,K] prior_cov;
}
parameters {
vector[K] beta;
}
model {
y ~ bernoulli_logit(x*beta);
beta ~ multi_normal(prior_mean, prior_cov);
}