Bayesian Estimation of Parameter of Binomial Distribution with Multiple Change Points for Left Truncated and Right Censored Data

By filling in the missing data of the life variable, the complete-data likelihood function of binomial distribution for left truncated and right censored data is obtained. The full conditional distributions of change-point positions and other parameters are given. Every parameter is sampled from the full conditional distributions respectively, using MCMC method of Gibbs sampling together with Metropolis-Hastings algorithm. The implementation steps of MCMC method are introduced in detail. Gibbs samples of the parameters are obtained, and the means of Gibbs samples are taken as Bayesian estimations of the parameters. The random simulation test results show that Bayesian estimations of the parameters is fairly accurate.