I read that if the data is normally distributed with mean $\mu$ and variance $\sigma^2$ (both unknown) then to have the joint posterior distribution $p(\mu, \sigma^2 | y)$ in closed form, one has to use a inverse gamma prior for variance $\sigma^2$ and a conditional conjugate prior for mean $\mu$. But most of the examples of implementations in books that I see are in the following way
for(i in 1:n){
y[i]~dnorm(mu, precision)
}
mu~dnorm(0, 0.0001)
precision~dgamma(0.0001,0.0001)
Here the marginal prior $p(\mu)$ is normally distributed. Shouldn't the marginal prior $p(\mu)$ be specified to be t-distributed? so that the conditional conjugate prior of $\mu$ is normally distributed and so that the joint posterior is in closed form?