Bayesian Estimation Of Parameter Survival Regression Models Based On MCMC Method

In this thesis,Bayesian estimation is performed by MCMC method for different parameter survival regression models.This thesis discusses univariate and multivariate parametric survival models(survival data is right-censored).When the prior distribution of parameters is taken as a normal distribution or a t distribution,respectively according to their likelihood function,the joint posterior distribution density can be derived.And then this thesis uses R language to generate random data of the model and analysis by R language software package to test the model of the parameters' estimated results using Bayesian analysis.Afterwards,actual cases analysis is performed.The MCMC method is used by WINBUGS software to demonstrate how to carry out the Bayesian analysis of parameters iteratively,and different initial values will be input to form different Markov chains.If the Markov chains tend to be steady and the statistical estimation of the parameters is good,these prove that the model is effective.In addition,by selecting different prior distributions of the parameters,the validity of several parameter survival models under the same set of data and different prior distribution of parameters will be compared.The models used in this thesis are mainly parameter survival regression models,including single-parameter survival analysis regression models and multivariate parametric survival analysis regression models,they are exponential regression model,Weibull regression model,extreme value regression model and log-normal regression model.In the part of numerical simulation,Each survival regression model is established using R language software,and random numbers are generated based on the model and Bayesian estimation is performed using R packages.In the case analysis,Bayesian analysis is mainly performed by the Gibbs sampling and the Metropolis–Hastings algorithm in the Markov Chain Monte Carlo(MCMC).The basic principle is to sample from the full-condition probability distribution.A Markov chain is then generated and the parameters are estimated by iteration.The Markov Chain Monte Carlo process(MCMC)can be more easily and quickly implemented by WINBUGS software,and the suitability of the model can be judged by using the DIC values generated by the WINBUGS after iteration.Finally,the DIC values of different models and parameters in different prior distributions of different sets of data are used to compare the suitability of these models.