I asked this question on mathoverflow yesterday and got a suggestion to try it here. I apologize if this is an easy question, but I can't seem to find an answer anywhere.
I'm trying to duplicate a macroeconomic paper that uses MCMC analysis to derive time series and parameter values. For the variance of a white noise term the authors of the original paper choose an inverse gamma prior of mean 0.5 and having a 90% confidence interval between 0.21 and 0.79.
I'm using Dynare to run my estimation and Dynare only accepts these kinds of parameters in terms of standard error. Therefore, my question basically amounts to "how do I find the square root of an inverse gamma distribution"?
In case it's not clear what I'm asking, here's how the model equation appears in the paper:
$a_t$ follows a simple AR(1) process and $\epsilon_a$ is meant to be white noise with mean 0 and variance $\sigma_a$. The prior for $\sigma_a$ is supposed to follow an inverse gamma distribution with the mean and confidence interval above. My question then is how can I find the "square root of the distribution" so I can write an expression for the standard error of $\epsilon_a$, instead of its variance?
If it's not possible to come up with a simple expression for this, would you have any suggestions for roughly equivalent specifications of the prior?
Thanks in advance