In certain models, we are expected to evaluate the variance of the posterior (e.g. Linear regression with ARD) using a hyper-prior. Usually, I have seen that Half-Cauchy hyper-prior is used in such occasions, due the certain proprieties of the variance (because variance is always > 0 ).

However, Edward does not implement Half-Cauchy distribution. Therefore, what should be a suitable distributions to consider as the distribution of the variance when performing the KLqp?

Thanks