A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches
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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BibTeX
@misc{zhao2026bernsteinbinomial,
title = {{A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches}},
author = {Yuan-Fan ZHAO and Yikai GUO and Xun-Jian LI and Man-Lai TANG and Guo-Liang TIAN},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04964},
eprint = {2610.04964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04964},
}
RIS
TY - UNPB
TI - A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches
AU - Yuan-Fan ZHAO
AU - Yikai GUO
AU - Xun-Jian LI
AU - Man-Lai TANG
AU - Guo-Liang TIAN
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04964
UR - https://arxiv.org/abs/2610.04964
AB - 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.
ER -