🤖 AI Summary
This study addresses the overdispersion problem in finite discrete count data and the limitations of the Beta-binomial model, including its subjective prior specification and fitting bias. To overcome these issues, this work proposes the Bernstein-binomial model. By leveraging the uniform approximation property of Bernstein polynomials, the method constructs a highly flexible prior framework that transcends traditional unimodal constraints, dynamically adapts to complex data structures, and supports both frequentist and Bayesian inference as well as regression extensions. Simulation experiments and empirical analyses demonstrate that the proposed model significantly outperforms existing methods in terms of fitting accuracy, robustness, and predictive performance.
📝 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.