Overdispersed alternative to multinomial

Tamas_Papp
Sat, 13 Dec 2025 16:48:04 +0000
Statistics

I have a multilevel Bayesian model where (a_i, b_i, c_i) = f(\theta_i) for each unit i = 1, \dots, 1000, which are latent variables, f comes from a model.

For each i, and j = 1, 2, 3, I observe (A_{i,j}, B_{i,j}, C_{i,j}), where

1. A, B, C are positive integers, summing to K (eg K = 80 or similar),

2. are IID given i,

3. E[A_{i,j}] = a_i, E[B_{i,j}] = b_i, E[C_{i,j}] = c_i,

The multinomial distribution would be ideal for this, except that I found that my data has much more dispersion.

I am looking for a cheap way to implement an overdispersed discrete distribution with these properties + at least one parameter to control overdispersion (actually one would be plenty). I only need logpdf (should be ADable, fast, A,B,C are data), and rand (for checking, can be slow). I looked at various papers but they involve a latent variable, which would blow up my parameter space.

3 posts - 2 participants