hey @bwengals I just went through the Simpson paper on the PC prior and your notebook, really fantastic stuff! I think I’ve got the main idea: you’re using KL divergence to measure how far an over-dispersed model (with dispersion parameter \alpha) deviates from a base Poisson model. That makes sense to me.
Where I’m getting a bit stuck is in how you set the two free parameters that define the PC prior. In your notebook, you write:
\alpha \sim 1 / \text{Weibull}(x, a=0.5, b=1/\lambda^2)
I follow that part, but I’m not sure how you determine $lambda$. You define it as:
-\log(\epsilon) / d_{KL}(L^{-1})
Could you help me interpret what \epsilon and L represent in this context? From your inset plot, it seems like L might set the mode of \alpha, and \epsilon controls how much prior mass falls below that mode—but that’s just my guess.
How do you typically choose \epsilon and L in practice, based on your data or modeling goals? Any tips or references would be super helpful!