Acceleration of Monte Carlo EM Algorithm

EM algorithm is one of the data augmentation algorithms, which usually are used to obtain estimate of the posterior mode of observed data recent years. However, because of its difficulty in calculating the explicit expression of the integral in E step, the application of EM algorithm is limited. While Monte Carlo EM algorithm solves the problem well. Owing to effectively facilitating the integral in E step of EM algorithm by Monte Carlo simulating, Monte Carlo EM algorithm has been successfully used to a wide range of applications. There is, however, the same shortage for EM algorithm and Monte Carlo EM algorithm, that the convergence rate of the two algorithms is linear. So this paper proposes the acceleration of Monte Carlo EM Algorithm, which is based on Monte Carlo EM Algorithm and Newton-Raphson algorithm, to improve the convergence rate. Thus the acceleration of Monte Carlo EM Algorithm has the advantages of both Monte Carlo EM Algorithm and Newton-Raphson algorithm, that is to say it facilitates E step by Monte Carlo simulation and also has quadratic convergence rate in a neighborhood of the posterior mode. Later its excellence in convergence rate is illustrated by a classical example.