Bayesian Estimation Of Parameter Change Points Of Exponential Distribution Family Under IIRCT

In recent years,Change point problem has gradually become a hot topic in the field of statistics,and both theoretical research and practical application have been rapidly developed.Scholars at home and abroad,such as Csorgo,Professor Wang Liming,Professor Miao Boqi and Professor Chen Xiru,have conducted in-depth research on the change point problem and have a profound impact on it.The application has also been extensive,from the initial industrial quality control to the natural world,political economy,medicine and health,etc.There are many methods to study the change point problem,such as least square method,Bayes method,non-parametric method,maximum likelihood method and so on.In recent years,most scholars have tended to adopt the Bayes method,which can fully and profoundly recognize the position of the change point,and the model inference is more efficient and accurate.Exponential distribution family plays an important role and occupies an important position in statistical inference.It is a kind of important distribution family,which is widely used in various fields.The Gamma distribution,Normal distribution,Rayleigh distribution and Poisson distribution belong to the exponential distribution family.First,it introduces the research background and current situation of change point problem at home and abroad,and also briefly introduces the exponential distribution family.Secondly,it introduces some preliminary knowledge about Bayes,including the origin and development of Bayes,prior distribution,Bayes formula and posterior distribution.Then,the IIRCT model is briefly introduced,and the complete data likelihood function of the exponential distribution and the normal distribution in the exponential distribution family is given.The full conditional distribution is obtained by selecting the prior distribution of each parameter.Finally,the MCMC method is introduced,and the parameters of exponential distribution and normal distribution were analyzed by Gibbs sampling and simulation.The MCMC method is effective for data truncation.