A Random-Discretization Based Monte Carlo Sampling Method And EM Algorithm Applied In Grouped Data

Recently , Monte Carlo methods , for example , Markov Chain Monte Carlo(MCMC) . importance sampling and data-augmentation , have been developed for numerical sampling and integration in statistical inference, especially in Bayes analysis .As dimension increases , problems of sampling and integration can become very difficult. So FU and WANG (2002) showed us a method of computing the approximate likelihood estimates and integration. It is based on the concept of random discretization of density function with respect to Lebesgue measure. And called it a Random-Discretization Based on Monte Carlo Sampling Method.In this manuscript, I applied this method into grouped data statistical inference, and improved it . Grouped data is a very common type of incomplete data in life tests . usually it is difficult to make Bayes analysis because of the complication of likelihood function. In this text , 1 simulated the grouped data with several methods . First , I used the Random-Discretization Based on Monte Carlo Sampling method , and computed the estimation of the unkown parameters and the 95% interval estimation . The attraction of this method is its simplicity and ease of implementation. One of the great strengths of this method is that it requires only the knowledge of the functional form of the density function up to an unknown normalizing constant. In this manuscript, I also improved this method. And used the improved method to simulate . Then, I computed the estimation of unknown parameters through EM algorithm. Finally , I compared the simulated results of different, methods , and compared with the results of Zhong Liu and ShiSong Mao(1997). The results show us that the Random-Discretization Based on Monte Carlo Sampling Method performs better than Gibbs sampler and other methods, and the improved method is better than the Random-Discretization Based on Monte Carlo Sampling Method, especially for vy.