Estimation of highly heterogeneous multinomial probabilities observed at the beginning of COVID-19

Abstract

The daily counts of COVID-19 cases differed significantly from one region to another at the beginning of the COVID-19 pandemic in any given country. The disease first hit some regions before spreading to others. The Poisson distribution is frequently used to analyze disease occurrence in certain locations at certain times. However, in highly heterogeneous situations, the estimator of multiple Poisson means is not close to the actual population parameter. The estimator of multinomial probabilities under an existing prior is also not close to the actual population parameter in highly heterogeneous situations. We propose a Bayesian estimator of multinomial probabilities under a data-dependent prior. This prior is built using zeta distribution coefficients and depends only on the rank of data. Using simulation studies, the proposed estimator is evaluated with two well-known risks. Finally, the daily counts of COVID-19 cases are analyzed to show how the proposed estimator can be used in practice.