半参数双重Tweedie复合泊松回归模型的贝叶斯分析  

A Semiparametric Bayesian Approach to Double Tweedie Compound Poisson Regression Model

作　　者：段星德 伍震寰 张钟妮 张文专[1] DUAN Xingde;WU Zhenhuan;ZHANG Zhongni;ZHANG Wenzhuan(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数学与统计学院,贵州贵阳550025

出　　处：《应用数学》2024年第1期272-279,共8页Mathematica Applicata

基　　金：国家自然科学基金项目(12161014);全国统计科学研究项目(2021LY011);贵州省省级科技计划项目资助(黔科合基础[2020]1Y009);贵州省教育厅自然科学基金资助项目(KY[2021]134)。

摘　　要：为了分析健康保险行业中出现的半连续卫生保健费用数据,本文提出一类半参数双重Tweedie复合泊松回归模型.在分析中,首先采用修正鞍点逼近的数值方法去近似Tweedie复合泊松分布的密度函数;其次,利用Gibbs抽样技术和Metropolis-Hastings(MH)算法的混合算法获得了模型参数的联合贝叶斯估计;最后,给出了几个模拟研究以及把这些方法用来分析兰德健康保险实验中的卫生保健费用数据.We introduce a new class of semiparametric double generalized linear models based on Tweedie Compound Poisson distribution,accommodating semicontinuous health care cost data in the health actuarial field.Firstly,a modified saddle-point approximation approach is used to evaluate the density function of the Tweedie’s Compound Poisson distribution.In addition,a hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is proposed for producing the joint Bayesian estimates of unknown parameters and nonparametric function.Finally,several simulation studies and a real example with the RAND Health Insurance Experiment are presented to illustrate the proposed methodologies.

关 键 词：卫生保健利用 复合泊松分布 半连续数据 MH算法 GIBBS抽样 贝叶斯P-样条 

分 类 号：O212.8[理学—概率论与数理统计]