Prior Parameters in Bayesian Hierarchical Linear model I'm trying to fit a linear model to describe student performance in 2 different schools. 
My response variable is $$Y_{ij}= X_{ij}*\beta+Z_{ij}*\gamma_j + \epsilon_{ij}$$ .
$$i = 1,...,n $$ 
$$j = 1,2 $$
$\beta $ are the fixed parameters, 
while $\gamma_j$ is the vector of mixed ones.
$\epsilon_{ij}$ ~ $N(0,\sigma^2)$
$\sigma^2$ ~ $Inv-Gamma(a,b)$
$\beta$ ~ $N_p(b_0,B_0)$
$\gamma_j$ ~ $N_p(0,\Sigma)$
$\Sigma$ ~ $Inverse-Wishart(S_0^{-1},\eta_0)$ . 
In my model $X_{ij}$ and $Z_{ij}$ are the same, so that to each predictor is associated a fixed and a random effect.
I've tried to implement this model both with MCMChregress function in R and $Jags$, but unfortunately I can't find any literature regarding the parameters of my mixed effects (for $\beta$ I used an uninformative prior and then I cheated using the ols estimates, but I still get no significance in my mixed effects ).
 A: Part of your issue could be that you only have two schools, so there's not much information at the school level. (You're trying to determine gamma with essentially two data points.) I've read that as a rule of thumb you want five or more groups, and your non-significance could simply be that you don't have enough information to nail down your coefficients.
You could add strong priors, but then the priors will be driving things. If you have principled priors, that could be an option, otherwise not.
If you are running into convergence problems -- you have checked for proper convergence, right -- weak priors (say a wide Normal) can help because uniform priors throw a ridiculous amount of weight to +/- infinity, which is probably not reasonable.
I'd also recommend using the brms package in R. It uses Stan under the hood and along with rstanarm is the cutting edge of Bayesian modeling in R.
EDIT: In terms of the number of groups required for good group-level estimates, see papers like: http://joophox.net/publist/methodology05.pdf and I'm also pretty sure it's mentioned by Gelman, but can't find it right now.
