I’ve managed to trade one problem for another. Using the jgamma function from above, I now perfectly retrodict \nu, but the \gamma estimate is worthless (thought it also runs faster now, which is kind of fun). Here’s the plot:
From the traceplots it appears that the NUTS doesn’t sample above values close to 0, which is a problem because we need it to find values as high as 2 or 3 (to be sure that all reasonable values will be received).
To check if this was the result of poor priors, I performed a prior predictive check, and produced the following results. The red are the parameters from the previous figure to make sure they are within a high probability range of the prior:
So now I’m doubly stumped. From the pairs plot (below), it looks like the issue is that nu and lambda are now more correlated than ever.
So it seems to me that either the Johnny parameterization did something really funky and unexpected to my model, or (more likely) I implemented it wrong in my jgamma function. If anyone has any thoughts, I’m all ears! I’m looking forward to hearing your ideas.