广义混合Poisson线性模型的贝叶斯推断

Bayesian Inference of Generalized Mixed Poisson Linear Models

该文在贝叶斯框架下研究广义混合Poisson线性模型的变量估计和变量选择问题.首先结合广义Poisson线性模型和GMM模型,构造混合广义Poisson线性模型,并给出似然函数,然后构造未知参数的先验,给出后验似然函数,随后通过后验似然与先验的乘积得到未知参数的满条件分布,用Gibbs算法和M-H抽样算法抽取未知参数得到参数的估计值,并运用二元潜变量标记活跃变量,假设未知先验,给出后验似然,通过Gibbs算法和M-H抽样算法挑选出回归系数,最后进行数值模拟验证贝叶斯估计的有效性和变量选择的准确性.

Based on the Dirichlet distribution,a generalized mixed Poisson linear model is constructed,and the posterior likelihood function is obtained by assuming a prior of unknown parameters.First,obtain the full conditional distribution of unknown parameters by multiplying posterior likelihood with prior.Then,extract unknown parameters using Gbbis algorithm and M-H sampling algorithm to obtain estimated values of parameters,and select regression coefficients.Numerical simulations have verified the effective-ness of Bayesian methods in estimating the parameters of generalized mixed Poisson linear models and the correctness of selecting regression coefficients.