# What prior distribution of parameters in the Bayesian estimation of a GARCH model?

In the case of the Bayesian estimation of GARCH(1, 1) model with Student–t or a Skewed distributions for innovations, is it more correct to assume a uniform distribution for the parameters or to assume the truncated Normal prior?

In other word, what is the difference between the following two settings that are usually found in the literature? Why do we assume a normal as a prior distribution?

    model{
for (t in 1:N){
y[t] ~dt(mu, tau[t], nu)
a[t] <- y[t] - mu
tau[t] <-1/h[t]
}
for (t in 2:N){
h[t] <- alpha0 +alpha1 * pow(a[t-1],2)+ beta1 * h[t-1]
}

#prior

mu ~ dnorm(0, 0.001)
h[1] ~ dunif(0, 0.0012)
alpha0 ~ dunif(0, 0.2)
alpha1 ~ dunif(0.00001, 0.8)
beta1 ~ dunif(0.00001, 0.8)
nu ~ dunif(1,30)


or

#prior 2
mu ~ dnorm(0, 0.001)
h[1] ~ dunif(0, 0.0012)
alpha0 ~ dnorm(0, 0.001)I(0,)
alpha1 ~ dnorm(0.00001, 0.001)I(0,)
beta1 ~ dnorm(0.00001, 0.001)I(0,)
nu ~ dnorm(0,0.001)I(0,)