Yes, I’m working with species abundance data which was one of the original uses of the model, before it’s rediscovery by Pitman & Yor [1]. It seems that the stick breaking aspect can be implemented in Stan, but it would also require size biased resampling to recover the Pitman-Yor process, which would be impossible to do in Stan. No?
Exactly, even with \alpha < 1, it seems that the data is not getting close enough to edge of the simplex. Abundant species do not appear abundant enough in the posterior, less abundant species appear too abundant.
@betanalpha That makes sense. One question about parameterization though. It seems like this would be the same model as the normalized generalized inverse Gaussian, but with a different posterior geometry. However, I know that you have written before these normalized models can cause problems. I’m curious why this parameterization works better or are there scenarios when the normalization parameterization would work better or are these not actually the same model?
[1] Engen, S. (1978). Stochastic Abundance Models. (S. Engen, Ed.). London: Chapman and Hall Ltd.