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arXiv · 2610.04964

A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches

Yuan-Fan ZHAO·Yikai GUO·Xun-Jian LI·Man-Lai TANG·Guo-Liang TIAN
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Abstract

Finite discrete count data are ubiquitous in fields such as biomedicine and social sciences and these data frequently exhibit over-dispersion, rendering the binomial distribution inadequate for modeling. Although the beta-binomial distribution mitigates this by assigning a subjective beta prior to the success probability, its reliance on a pre-specified parametric shape may result in biased representations of prior information, failing to capture the complex and heterogeneous characteristics of real-world data. To address these limitations, this paper proposes a novel Bernstein-binomial model. By leveraging the uniform approximation properties of Bernstein distribution, we construct a highly flexible and general prior framework for the success probability in binomial distribition, which dynamically adapts to complex data structures, avoiding the subjectivity and restrictions associated with conventional unimodal priors. A comprehensive theoretical framework for both frequentist and Bayesian inferences is established. Furthermore, the model is extended to a regression setting to account for covariate effects. Extensive simulation studies and real-world data applications confirm that the proposed Bernstein-binomial model significantly outperforms existing models. It offers superior fitting accuracy, robustness, and out-of-sample predictive performance when modeling over-dispersed counts with complex latent prior structures.

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Yuan-Fan ZHAO, Yikai GUO, Xun-Jian LI, Man-Lai TANG, Guo-Liang TIAN. 2026-10-04. A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches. https://arxiv.org/abs/2610.04964

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