I want to use a t distribution to model short interval asset returns in a bayesian model. I’d like to estimate both the degrees of freedom (along with other parameters in my model) for the distribution. I know that asset returns are quite non-normal, but I don’t know too much beyond that.
What is an appropriate, mildly informative prior distribution for the degrees of freedom in such a model?
On page 372 of ARM, Gelman and Hill mention using a uniform distribution on the inverse of DF between 1/DF = .5 and 1/DF = 0.
Specifically, in BUGS, they use:
nu.y <- 1/nu.inv.y nu.inv.y ~ dunif(0,.5)