Declaring constrained parameters

let me narrow down my question a bit more. Basically I am deriving the beta parameters in a logistic regression.
Exp(alpha + gamma * z) / 1+ exp(alpha + gamma * z)

Gamma is a vector w a small mean and variance.

My question is how best to declare the gamma variable. Ideally I would use a Gaussian prior, but I would not know what to put down as it’s mean. So instead I am using the default uniform prior. Would a Gaussian prior have converged faster? If so how would I declare a Gaussian prior wo knowing the mean?

The posted code has a time series added to the logistic regression, but the basic question is still on gamma parameters themselves.