用于拟合过度离散计数数据的贝叶斯Bell回归模型及其应用
Bayesian Bell regression model for fitting of overdispersed count data with application
AI总结：
本研究针对过度离散计数数据的分析需求，提出结合G-先验与平坦正态先验的贝叶斯Bell回归模型，经模拟与真实数据验证，G-先验估计效果更优，为计数数据分析的先验选择提供参考。
摘要：
Bell回归模型（BRM）是一种常用于分析存在过度离散特征的计数数据的统计模型。本研究提出了BRM的贝叶斯分析方法，并为其应用提供了新视角。具体而言，我们除了引入平坦正态先验分布外，还为BRM的贝叶斯推理引入了G-先验分布。为对比所提先验分布的性能，我们开展了模拟研究，结果表明G-先验分布能为BRM提供更优的估计效果。此外，我们将该方法应用于真实数据，并借助多种模型选择准则将BRM与Poisson回归模型进行对比。研究结果为贝叶斯方法在BRM估计与推理中的应用提供了宝贵见解，同时凸显了计数数据分析中考虑先验分布选择的重要性。
英文摘要：
The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application. Specifically, we introduce a G-prior distribution for Bayesian inference in BRM, in addition to a flat-normal prior distribution. To compare the performance of the proposed prior distributions, we conduct a simulation study and demonstrate that the G-prior distribution provides superior estimation results for the BRM. Furthermore, we apply the methodology to real data and compare the BRM to the Poisson regression model using various model selection criteria. Our results provide valuable insights into the use of Bayesian methods for estimation and inference of the BRM and highlight the importance of considering the choice of prior distribution in the analysis of count data.
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