Is there an inverse / reciprocal / log-uniform distribution in PyMC?

Questions
1

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?

2

You can just use tt.exp(pm.Flat("logval")).
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.

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3

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!

4

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.

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