# Computing the Dirichlet-Multinomial Log-Likelihood Function

arXiv: https://arxiv.org/abs/2007.11967 · HTML: https://mlsanity.com/paper/2007.11967/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Etat de l'art sur l'application des bandits multi-bras](https://mlsanity.com/paper/2101.00001/) (2021)

## Abstract (arXiv)

Dirichlet-multinomial (DMN) distribution is commonly used to model over-dispersion in count data. Precise and fast numerical computation of the DMN log-likelihood function is important for performing statistical inference using this distribution, and remains a challenge. To address this, we use mathematical properties of the gamma function to derive a closed form expression for the DMN log-likelihood function. Compared to existing methods, calculation of the closed form has a lower computational complexity, hence is much faster without comprimising computational accuracy.