Yeah, I came across that thread. as well. It seemed like the main difficulty was that it required a line-search step, but that wouldn’t go away with a fixed shape parameter. @sakrejda mentioned the closed-form chi-squared approximation, but that is still an approximation for the chi-squared (though it appears a different one from my reference in the original post).
It seems like this would be the same model and wouldn’t address the need for varying stepsizes. Is the idea here just to make things more numerically stable for small values?
@sakrejda I’m a bit confused what is going on in your code. What is the gamma_lpdf_1S function?
I’m trying to get a bit more intuition behind this - to me, why wouldn’t we expect to see the same pathologies in the tails of the cauchy to come up in the tails of the gamma?