EM Algorithms For Parameter Estimation Of Some Hierarchical Models

Maximum Likelihood Estimation(MLE)is a method for estimating distribution parameters.This method finds the parameter value that maximizes the likelihood function.It is the most commonly used estimator solution method at present.Data missing is common in experiments,traditional method will encounter many difficulties in dealing with missing data parameter estimation problems,such as inaccurate estimation results,complex likelihood function.Using iterative method,the EM(Expectation—Maximization)algorithm solved these problems well.In this paper,the EM algorithm for parameter estimation of several hierarchical models is studied.The feasibility of the proposed methods is verified by numerical examples or numerical simulations.The main contents are as follows:1.The parameter estimation problem of Poisson-multinomial model is studied,and the MLE of parameter and iterative equations of EM algorithm are given.Through the data of a group of leukemia patients,the maximum likelihood estimation and EM algorithm parameter estimation results in the case of missing data are compared.2.The analytical expressions of the multiple Poisson model's MLE in the case of complete data are derived.The iterative equations of EM algorithm for parameter estimation of missing data cases are given,and the effectiveness of the EM algorithm is illustrated by an example.3.The observed data is regarded as incomplete data,and the iterative sequence of the EM algorithm of binomial-Poisson model is derived.The model is extended to three layers to obtain the binomial-Poisson-exponential model.The parameter estimation problem of the extended model is studied.Estimate the problem.The simulation was carried out by R software to verify the feasibility of EM algorithm.