EM Algorithm for Normal Mixture Likelihoods

The purpose of the study is to use the expectation-maximization (EM) algorithm for finding the maximum likelihood estimates (MLEs) under the normal mixture models in which allow heterogeneity in forms of the multi-nodes, skewed, long-tailed, and/or contaminated distributions. The motivational application of the standardized morbidity ratio (SMR) of geographical HIV/AIDS data displaying on a map among all study provinces in Thailand 2013 is illustrated. The results showed that the normal mixture model fitted data well with the nice MLEs corresponding to the EM algorithm coping with good yielding both numerically stable convergence and the fine estimates of local maximum points. Another advantage of EM algorithm was in adding up the latent unobserved probabilities of each study province belonging to the component of normal mixture in solving the problem of the incomplete data while other algorithms, such as Newton-Raphson and Fisher Scoring, couldn't be able to augment those unobserved missing data. However, EM algorithm seemed to have slow convergence.