On Non- and Weakly-Informative Priors for the Conway-Maxwell-Poisson (COM-Poisson) Distribution

Abstract: Previous Bayesian evaluations of the Conway-Maxwell-Poisson (COM-Poisson) distribution have little discussion of non- and weakly-informative priors for the model. While only considering priors with such limited information restricts potential analyses, these priors serve an important first step in the modeling process and are useful when performing sensitivity analyses. We develop and derive several weakly- and non-informative priors using both the established conjugate prior and Jeffreys' prior. Our evaluation of each prior involves an empirical study under varying dispersion types and sample sizes. In general, we find the weakly informative priors tend to perform better than the non-informative priors. We also consider several data examples for illustration and provide code for implementation of each resulting posterior.