An empirical comparison of EM, SEM and MCMC performance for problematic Gaussian mixture likelihoods

We compare EM, SEM, and MCMC algorithms to estimate the parameters of the Gaussian mixture model. We focus on problems in estimation arising from the likelihood function having a sharp ridge or saddle points. We use both synthetic and empirical data with those features. The comparison includes Bayesian approaches with different prior specifications and various procedures to deal with label switching. Although the solutions provided by these stochastic algorithms are more often degenerate, we conclude that SEM and MCMC may display faster convergence and improve the ability to locate the global maximum of the likelihood function.