There has been growing awareness recently that conventional models for count data, such as the Negative Binomial model and zero inflated models, often yield poor fit and sub-optimal performance when applied to real-world count data problems. In response, a new, more flexible model for count data, the Poisson-Beta model, has started to attract attention. The Poisson-Beta model is a Poisson mixture where the underlying mixing distribution is a scaled Beta density. However, because its density function cannot be expressed in closed form, its use has been limited to very simple applications such as parameter estimation. This work presents a method of overcoming the computational complexity issues associated with the Poisson-Beta density to allow its application to problems of far greater complexity, enabling it to be used to model response variables in multivariate regression. This work additionally demonstrates that Poisson-Beta regression compares favorably to a range of commonly used regression models for count response data, achieving narrower confidence intervals and superior power.
Alan Herschtal (2025) studied this question.