Bayes Estimation Of Change-Point Model Of ??????? Distribution

Change-point problem is a significant research topic in the field of statistics all the time,which is applied in all fields of nature and society.In recent years,many statistical scholars have studied the change-point problem by using the method of Bayesian theory.Consequently,building on the foundation of our predecessors,the change-point in the ???????distribution model is studied based on the Bayes method.Primarily,on the basis of understanding the basic theory of change-point,four common methods of researching change-point are introduced,for example,Maximum Likelihood Estimation,Least Squares Estimation,Cumulative Sum of Squares Method and Bayes Estimation.The Bayes method is introduced in detail,including Bayes formula,the selection of prior distribution,the calculation of posterior distribution and two sampling methods based on Bayes theorem.Secondly,the change-point problem of the ??????? model is discussed by using Bayes method.According to the different detection data,we get the Bayes estimation of the single change-point in the model by starting from the full sample data.Using the two algorithm theories of the Bayes method,we write R language program for simulation verification and do the final estimation and data analysis of parameters.Then,the Bayes estimation of the change-point model was carried out under Randomly Truncated and Censored Data and IIRCT(Random Censoring Test model with Incomplete Information).According to the posterior distribution and the full conditional distribution of each parameter,the numerical simulation is carried out.The results show that under different sample data,the two algorithms can estimate the position of change-point well,and the parameter estimation is more accurate.By comparison,the IBF(Inverse B ayes Formulae)algorithm takes much less time to run than Gibbs sampling.Finally,research conclusions are obtained and research contents are further explained.