半连续纵向数据下Tweedie复合泊松部分线性混合效应模型的贝叶斯分析

Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models for Longitudinal Semicontinuous Data

在贝叶斯框架下,文章发展一类半参数Tweedie复合泊松部分线性混合效应模型来分析半连续纵向数据,并用贝叶斯P-样条来逼近模型的非参数函数.由于Tweedie复合泊松分布的密度函数没有显示表达式,这通常给计算带来困难,文章利用数据扩充法的思想,引入一个潜变量,可得到半连续随机变量和潜变量的联合概率密度函数,并基于这个联合概率密度函数进行贝叶斯统计推断.进一步,结合Gibbs抽样与Metropolis-Hastings(MH)算法的混合算法可得到模型的参数、随机效应以及非参数函数的联合贝叶斯估计以及潜变量的预测值.最后,通过模拟研究与实例分析来验证所提出方法的有效性.

Under the Bayesian framework,this paper develops a Tweedie compound Poisson partial linear mixed model on the basis of Bayesian P-spline approximation to nonparametric function for longitudinal semicontinuous data.It is quite difficult to directly implement Bayesian computation because the probability density function for Tweedie compound poisson distribution is not analytically tractable.Therefore,inspired by the data-augmentation strategy,we introduce a latent variable to obtain the joint probability density function of a semi-continuous random variable and the latent variable,and conduct the Bayesian statistical inference based on this joint probability density function.Furthermore,a hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is proposed for producing the joint Bayesian estimates of unknown parameters,random effects and nonparametric function,as well as the predicted value of latent variables.Finally,several simulation studies and a real example are presented to illustrate the proposed methodologies.