Computing the Dirichlet-Multinomial Log-Likelihood Function
This work addresses a computational bottleneck for statisticians and researchers using the Dirichlet-multinomial distribution for modeling over-dispersed count data, representing an incremental improvement.
The paper tackled the challenge of precise and fast numerical computation of the Dirichlet-multinomial log-likelihood function by deriving a closed-form expression using gamma function properties, resulting in lower computational complexity and much faster calculations without compromising accuracy.
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.