I'm trying to duplicate a macroeconomic paper that uses MCMC analysis to derive time series and parameter values. The authors of the original paper choose an inverse gamma prior for the variance of a white noise term. This distribution has a mean of 0.5 and 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) = rho_a * a(t-1) + epsilon_a

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?

Thanks in advance