Alternative EM methods for nonparametric finite mixture models

This research focuses on a general class of maximum likelihood problems in which it is desired to maximise a nonparametric mixture likelihood with fin itely many known component densities over the set of unknown weight paramet ers. Convergence of the conventional EM algorithm for this problem is extre mely slow when the component densities are poorly separated and when the ma ximum likelihood estimator requires some of the weights to be zero, as the algorithm can never reach such a boundary point. Alternative methods based on the principles of EM are developed using a two-stage approach. First, a new data augmentation scheme provides improved convergence rates in certain parameter directions. Secondly, two 'cyclic versions' of this data augment ation are created by changing the missing data formulation between the EM-s teps; these extend the acceleration directions to the whole parameter space , giving another order of magnitude increase in convergence rate. Examples indicate that the new cyclic versions of the data augmentation schemes can converge up to 500 times faster than the conventional EM algorithm for fitt ing nonparametric finite mixture models.