Trying to generalise the dirichlet-multinomial (non-analytical) framework (replacing Dirichlet with other distributions)

Modeling
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21

Just to make sure (I will have to generate random samples from this): the parametrisation you use is this?

image

https://pdfs.semanticscholar.org/bdb7/0423cea3717783ad5e6ac5c4f5577d257d01.pdf

22

It goes back to this paper:
“Size-biased discrete two parameter Poisson-Lindley Distribution
for modeling and waiting survival times data” by “Tanka Raj Adhikari, R.S. Srivastava”
http://iosrjournals.org/iosr-jm/papers/Vol10-issue1/Version-3/F010133945.pdf

Wasn’t the original posting a dirichlet-multinomial alternative?

23

Thanks

Indeed. I am following both the routes

  • mixed-multinomial, and the
  • mixed-poisson

As strange as it sounds, nothing seems to have been implemented for MCMC/HMC samplers that models long tail count data, that is most of real-world count data. Implementing from scratch is not a trivial task.

24

I let do the math my “algebra software”, check if the distributions sum up to 1. The problems arise
in multinomial models, log_sum_exp doesn’t perform really good. There’s no array based vector function.

I not yet wrote a script to combine the calculation of the derivatives with this expression optimization
package:

Even its not guaranteed that it results in the minimum expression terms, it performs quite good. Maybe worth a try to have a script to auto-generate Stan functions.