Tweedie复合泊松回归模型的Bayes估计和影响分析

Bayesian estimation and influence analysis of Tweedie’s Compound Poisson model

Tweedie复合泊松回归模型在精算科学,环境科学等领域有广泛的应用.为了研究Tweedie复合泊松回归模型的Bayes估计,在模型中引入潜变量,并通过视潜变量为缺失数据以及应用结合Gibbs抽样技术和Metropolis-Hastings(MH)算法的混合算法,获得了模型的参数和潜变量的联合Bayes估计.在估计理论的基础上,提出了两类Bayes数据删除影响测度及其相应的算法.最后通过模拟研究和实例分析验证了所给方法的有效性.

Tweedie’s compound Poisson model is useful in actuarial science,environmental science as well as many other areas of research.To investigate the Bayesian estimates of unknown parameters in Tweedie’s compound Poisson model,the latent variable is incorporated into model.To treat latent variable as missing data,a hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is implemented to produce the joint Bayesian estimates of unknown parameters and latent variable.In addition,based on the estimation theory,two Bayesian case deletion influence measures in the proposed models are presented and those computationally feasible formulas are given.Several simulation studies and a real example are presented to illustrate the proposed methodologies.