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.

翻译：先前对Conway-Maxwell-Poisson (COM-Poisson)分布的贝叶斯评估中，关于该模型的非信息性先验与弱信息性先验的讨论较少。尽管仅考虑此类信息有限的先验会限制潜在分析的范围，但这些先验在建模过程中具有重要的初步意义，且在敏感性分析中具有实用价值。我们基于既有的共轭先验和杰弗里斯先验，开发并推导了多种弱信息性与非信息性先验。对每种先验的评估涉及不同离散程度和样本量下的实证研究。总体而言，我们发现弱信息性先验的表现通常优于非信息性先验。此外，我们通过若干数据示例进行说明，并提供了每种后验实现的代码。