Longitudinal Data Analysis Based On Bayesian Semiparametric Method

Practical Bayesian semi-parametric method has been developed in various back-grounds,this paper est,ablished a Bayesian semi-parametric regression model that gen-eralizes standard mixed models for longitudinal dat,a,which contains flexible mean function and autoregressive(AR)covariance structure.The AR structure is generally specified by using a Gaussian process(GP)with a covariance function.This paper considers the AR structure by using a wider model type,that is,first introduce AR structure into OU process,and then assign a nonparametric Dirichlet process(DP)priori to the covariance parameter ? of OU process,result,ing in a Dirichlet Process mix(DPM)for the OU process,and semi-parameterizes the stochastic process term in the model.In this paper,we use modern Bayesian statistical method to infer the posterior distribution of the pa.rameters in the model.In the process of solving the model,we use Bayesian theorem to derive the full conditional distribution of the unknown parameters,use MCMC algorithm to estimate the parameters,and judge the convergence of the sampling results.this paper considers both of MCMC sampling process and Bayesian variat,ional inference,then combines posterior sampling trend graph,energy graph and negative ELBO loss histogram to determine the convergence.Using the generality of the model,an estimate of four different covariance structures is provided,.It is observed that models without incorporate AR structure perform poorly in estimating covariance or correlation matrices.