  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.
