On classical and Bayesian inference for bivariate Poisson conditionals distributions: theory, methods and applications

• Published in: Communications in statistics. Simulation and computation Vol. 54; no. 5; pp. 1371 - 1383
• Main Authors: Arnold, Barry C., Ghosh, Indranil
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.05.2025; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Bayesian estimation; Bivariate analysis; Bivariate Poisson conditionals distribution; Conjugate priors; Conjugates; Gamma distribution mixtures; Maximum likelihood estimation; Maximum likelihood method; Poisson distribution; Simulation; Statistical inference
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2023.2282387

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in modeling such data. In this article, we consider the inferential aspect of a bivariate Poisson conditionals distribution for which both the conditionals are Poisson but the marginals are typically non-Poisson. It has Poisson marginals only in the case of independence. It appears that a simple iterative procedure under the maximum likelihood method performs quite well as compared with other numerical subroutines, as one would expect in such a case where the MLEs are not available in closed form. In the Bayesian paradigm, both conjugate priors and non-conjugate priors have been utilized and a comparison study has been made via a simulation study. For illustrative purposes, a real-life data set is re-analyzed to exhibit the utility of the proposed two methods of estimation, one under the frequentist approach and the other under the Bayesian paradigm.