零一膨胀负二项模型的客观贝叶斯分析

该文建立了贝叶斯模型，对零一膨胀负二项分布进行了客观贝叶斯估计.采用数据增广策略，基于完全似然函数，推导出零一膨胀负二项模型不同形式的reference先验，进一步证明了相应的后验分布是恰当的.在不同的样本量和不同的参数真值下，对3种reference先验的性能进行仿真与评估.最后，对于生物化学博士生发表论文数量的数据集，零一膨胀负二项模型能够达到较好的拟合效果.

The Objective Bayesian Analysis of Zero-and-One Inflated Negative Binomial Model

The Bayesian model is established and the objective Bayesian analysis of zero-and-one inflated negative binomial distribution is discussed in the paper.Using the data augmentation strategy and the full likelihood function,different reference priors of zero-and-one inflated negative binomial model are calculated and it is further shown that the corresponding posterior distributions are proper.For different sample sizes and parameter true values of the parameters,three different reference priors are evaluated through simulations.Finally,a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed model and method.