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

TL;DR

This paper explores inference methods for bivariate Poisson conditional distributions, comparing frequentist and Bayesian approaches, and demonstrates their application with real data and simulation studies.

Contribution

It introduces an iterative MLE procedure for bivariate Poisson conditionals and compares Bayesian priors, providing practical estimation techniques and applications.

Findings

Iterative MLE performs well compared to other methods.

Bayesian methods with conjugate and non-conjugate priors are compared.

Real data analysis illustrates the effectiveness of the proposed methods.

Abstract

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.