My data is a set of $N$ observations $y_i$.
I would like to estimate $\mu$ and $\sigma$ in the following model:
$y_i \sim \mathrm{Normal}(\theta, \sigma)$
$\theta \sim \mathrm{Normal}(\mu, \frac{\sigma}{N})$
$\mu \sim \mathrm{Normal}(??, ??)$
$\sigma \sim ???(??,??)$
I would like to perform an Empirical Bayes analysis. Would someone be able to help me and explain how I would go about parametrizing the priors for empirical bayes?