Bayesian Analysis Of Tweedie Skewed Random Effects Models

Tweedie composite Poisson distribution is common in epidemiology,biomedicine,actuarial science and other fields.Random effect model can be used to study repeated measurement data and longitudinal data and is widely used.However,with more and more data subject to non normal distribution,random effect model is gradually extended from normal random effect model to skewed random effect model.Tweedie skew random effect model can better reflect the real situation of skew data and improve the simulation fitting accuracy,so it is of great significance to study this kind of model.In this paper,under the framework of Bayesian statistical inference,we construct the Tweedie skew random effect model,study the parameter estimation and variable selection of the model,and apply it to the analysis of practical problems.The skew random effect model studied in this paper consists of the following two random effect models: one is the skew normal random effect model,the other is the skew random effect model.The research contents are as follows(1)In the Tweedie partial normal random effect model,because the probability density function(PDF)of the Tweedie compound Poisson distribution has no explicit expression,this part uses the joint probability density function of the Poisson distribution and gamma distribution to define the PDF of the Tweedie compound Poisson distribution,and uses the joint partial normal random effect model to obtain the joint likelihood function.Combined with the prior information,the posterior distribution of the model is derived by using the mixed sampling algorithm of MH algorithm and Gibbs sampling,and applied to data simulation and practical application.(2)In the Tweedie partial random effect model,the PDF of infinite series approximating the Tweedie compound Poisson distribution is used,the joint partial random effect model is used,combined with the prior information,the posterior of parameters is derived by using the mixed sampling algorithm,and the variables of the model are selected by using Bayesian lasso.