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.

翻译：贝尔回归模型（BRM）是常用于分析具有过离散特征的计数数据的统计模型。本研究提出对BRM进行贝叶斯分析，并为其应用提供新的视角。具体而言，我们引入了G-先验分布和平坦正态先验分布用于BRM的贝叶斯推断。为比较所提出的先验分布的性能，我们进行了模拟研究，结果表明G-先验分布能为BRM提供更优的估计结果。进一步地，我们将该方法应用于实际数据，并通过多种模型选择准则将BRM与泊松回归模型进行比较。研究结果为贝叶斯方法在BRM估计与推断中的应用提供了重要见解，并揭示了在计数数据分析中考虑先验分布选择的关键意义。