0-1膨胀泊松分布的客观贝叶斯分析及其应用

Objective Bayesian Analysis for Zero-and-one-infiated Poisson Distribution and Its Application

在公共卫生、道路安全等应用领域,经常会同时出现零观测值、一观测值较多的情况。为更好地拟合这类数据,本文提出了0-1膨胀泊松分布模型并进行了客观贝叶斯分析。采用数据扩充策略,基于完全似然函数,得到Jeffreys先验和reference先验,进一步说明了它们都是二阶概率.匹配先验和后验分布的恰当性。设定不同的样本量和参数真值,采用数值模拟方法对不同的无信息先验进行评估。最后,对新加坡军团菌感染数据集进行了分析,研究表明,基于客观贝叶斯分析的0-1膨胀泊松分布能够达到更好的拟合效果。

Count data with excess zeros and ones arise frequently in various fields such as public health and road safety.In this paper,a zero-and-one-inflated Poisson distribution model is proposed and the objective Bayesian analysis is carried.Based on data augmentation strategy and the complete likelihood function,the Jeffreys prior and the reference priors are derived for this model.It is further shown tliat they are second order probability matching priors and the posterior distributions are proper.For different sample size and different true values of the parameters,simulations are adopted to assess the performance of the different priors.Finally,one Singapore legionnaires disease data-sc^t is analyzed to illustrate the practicability of the proposed model and methods.