·92· 《数量经济技术经济研究》2005年第10期 一种基于MCMC稳态模拟的 贝叶斯索赔校正模型 林静韩玉启1 朱慧明2 (1.南京理工大学经济管理学院；2.湖南大学) 【摘要】Buhlmann模型是贝叶斯方法在经验费率厘定中最为著名的应用，然 而该模型在结构参数先验信息不足的情况下，并不能得出参数的无偏后验估计。本 文针对传统方法的不足，运用基于MCMC模拟的贝叶斯方法对历史数据进行校 正，通过Gibbs抽样构造出一种多层Poisson模型稳态分布的马尔可夫链，动态模 拟出索赔频率的后验分布以及缺失参数值的后验估计，改进了传统的索赔校正模 型，提高了计算的精度。利用WinBUGS软件包进行建模分析，证明了该模型的直 观性与有效性。 关键词贝叶新分析经验费率索赔频率MCMC模拟Gibbs抽样 中图分类号F840文献标识码A A Bayesian Emendation Model for Claim Frequency Based on MCMC Method Abstract:Buhlmann model is the most famous application of the Bayesian method for the experience rate making.However,by this model one cannot get the unbiased posterior estimation of the parameters when there is not sufficient pri- or information for the structural parameters.Aimed at the fault of the traditional methods,this paper discusses how to conduct a Markov Chain for a hierarchical Poisson model with Gibbs sampling by applying Bayesian approach to revise the his- tory data and get the posterior distribrtions of the claim frequency as well as the posterior estimation of the censoring parameters dynamically,as well as improve the precision of the numeration.Also this paper utilizes the WinBUGS package, which is based on the MCMC method,to prove the objebtivity and validity of the model. Key words:Bayesian Analysis;Experience Rating;Claim Frequency;MC- MC Simulation;Gibbs Sampling ①基金项目：中国博士后科学基金项目(20040350216)、国家杜科基金项目(04CT]J003)。 万方数据·92· 《数量经济技术经济研究》2005年第10期 一种基于MCMC稳态模拟的 贝叶斯索赔校正模型 林静1 韩玉启1 朱慧明1、2 ① (1．南京理工大学经济管理学院；2．湖南大学) 【摘要】Bnhlmann模型是贝叶斯方法在经验费率厘定中最为著名的应用，然 而该模型在结构参数先验信息不足的情况下，并不能得出参数的无偏后验估计。本 文针对传统方法的不足，运用基于MCMC模拟的贝叶斯方法对历史数据进行校 正，通过Gibbs抽样构造出一种多层Poisson模型稳态分布的马尔可夫链，动态模 拟出索赔频率的后验分布以及缺失参数值的后验估计，改进了传统的索赔校正模 型，提高了计算的精度。利用WinBUGS软件包进行建模分析，证明了该模型的直 观性与有效性。 词受叶斯分析 中图分类号F840 经验赘率 索赔频率M鼢丘C模拟&协s抽样 文献标识码A A Bayesian Emendation Model for Claim Frequency Based on MCMC Method Abstract： Bnhlmann model is the most famous application of the Bayesian method for the experience rate making． However， by this model one cannot get the unbiased poste“or estimation of the parameters when there is not sufficient pri— or information for the structural Darameters． Aimed at the fault of the traditional methods， this paper discusses how to conduct a Markov C|hain for a hierarchical Poisson model with Gibbs sampling by applying Bayesian approach to revise the his— tory data and get the posterior distribrtions of the claim frequency as well as the posterior estimation of the censoring parameters dynamically， as well as improve the precision of the numeration． A1so this paper utilizes the WinBUGS package， which is based on the MCMC method， to prove the obj ebtivity and validity of the model． Key words： Bayesian Analysis； Experience Rating； Claim Frequency； MC— MC Simulation；Gibbs Sampling ①基金项目：中国博士后科学基金项目(20040350216)、国家社科基金项目(04CTJ003)。 万方数据