一种基于无信息先验下泊松分布变点的贝叶斯估计

A Bayesian Estimation of Poisson Distribution Change Point Based on Non-informative Prior Distribution

文章在Zhang等人讨论的确定无信息先验分布方法的基础上,基于“变换不变性”原则推导出了Poisson分布参数的无信息先验分布,并以此研究了Poisson分布尺度参数变点模型的参数估计问题,结合Poisson分布的单变点模型,分别利用极大似然方法和贝叶斯方法进行研究,并使用R软件进行仿真模拟,模拟的结果表明,相比于极大似然方法,贝叶斯方法的估计值更加接近于真实值。并将此方法应用于英国煤灾事故数据集,实证分析的结果与前人研究的结果是基本一致的,证明用此先验分布对泊松分布变点问题进行研究是可行且精度较高的。

Based on the method of determining the non-informative prior distribution discussed by Zhang et al., the non-informative prior distribution of the parameters of Poisson distribution is derived based on the principle of“transformation invariance”, and the parameter estimation problem of the scale parameter change-point model of Poisson distribution is studied. Combined with the single change-point model of Poisson distribution, the maximum likelihood method and Bayes method are used respectively, and R software is used for simulation. Experimental results show that compared with the maximum likelihood method, and the estimated value of Bayes method is closer to the real value.This method is applied to the UK coal disaster data set, and the empirical analysis results are basically consistent with the results of previous studies, which proves that it is feasible and accurate to use this prior distribution to study the Poisson distribution change point problem.