Suitable Distribution for variance as a Hyperprior


#1

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


#2

How about using the TransformedDistribution model to create the necessary probability distribution?
http://edwardlib.org/api/ed/models/TransformedDistribution
We can create, for example, log-normal distribution using this model.
Similarly, can’t we create Half-Cauchy distribution?


#3

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.