Suitable Distribution for variance as a Hyperprior


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?



How about using the TransformedDistribution model to create the necessary probability distribution?
We can create, for example, log-normal distribution using this model.
Similarly, can’t we create Half-Cauchy distribution?


Yeah, I suppose we could do that.

I know how to implement log-normal using TransformedDistribution yet I’m not sure how to extend that for Half-Cauchy implementation.