Abstract
In the present study, we undertake the task of hypothesis testing in the context of Poisson-distributed data. The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate. We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem. Among these are the conditional test, the likelihood ratio test, and the Bayes factor. Additionally, we employ the posterior predictive p-value in our analysis, coupled with its corresponding calibration procedures. As the culmination of our investigation, we apply these diverse methodologies to test both simulated datasets and real-world data. The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies - Hong Kong and Rwanda. This allows us to provide a practical demonstration of the methodologies' applications and their potential implications in the field of epidemiology.