Dependence on a collection of Poisson random variables

TL;DR

This paper introduces two new hierarchical models to induce dependence among Poisson counts, enabling flexible temporal and spatial dependence structures with Bayesian inference, demonstrated through maternal mortality data analysis.

Contribution

The paper presents novel hierarchical models for dependent Poisson counts using latent variables, extending to overdispersion and spatial-temporal dependence.

Findings

Models successfully capture dependence in Poisson data.

Bayesian inference provides effective parameter estimation.

Application to maternal mortality illustrates practical utility.

Abstract

We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict stationarity as special case. Order--$p$ dependence is described in detail for a temporal sequence of random variables, however spatial or spatio-temporal dependencies are also possible. A full Bayesian inference of the models is described and performance of the models is illustrated with a numerical analysis of maternal mortality in Mexico. Extensions to cope with overdispersion are also discussed.