Four Methods of Estimating Parameters of a Gaussian Mixture Model

Gaussian mixture model is the most widely used finite mixture model. The important feature of this model is its flexibility with respect to various forms of continuous distributions. Because the most important part of model fitting is the estimation of its parameters, we want to estimate two-component Gaussian mixture model parameters through the four estimation methods. We introduce a two-component Gaussian mixture model and then estimate model parameters using the method of moment and maximum likelihood by the name of analytical and numerical solutions, respectively. In continuation, the parameters are estimated using the EM algorithm and the Gibbs sampler algorithm. In conclusion, the results of these methods are compared with each other. We try to solve an estimation problem with the four common methods and introduce advantage and disadvantage of them for users.