Many sources mention the non-informative prior 1/x, which is uniform on the log scale. This seems to be called the inverse, reciprocal, or log-uniform distribution, but I find no mention of this in either the PyMC or STAN documentations. It is trivial to add it as a Potential, but then it cannot be prior-post sampled from. Am I missing it somewhere?
You can just use
This is an improper prior just like Flat, so you can’t sample from it by definition.
I wouldn’t usually recommend using this prior unless you have good reason to. It assumes that your problem is perfectly scale invariant, which I would argue is usually not the case.
A half normal or half student-t is in most settings a better prior for scale parameters.
I know that the unbounded distribution is improper, but it can be given bounds, like the Uniform to make it proper. https://en.wikipedia.org/wiki/Reciprocal_distribution
Thanks for the tip though!
In that case it would be
tt.exp(pm.Uniform('logval', lower=-1, upper=3)).
But really, don’t do that unless you really know that you need this. This is definitely not best practice.