We are presently using a combination of Metropolis-Hastings, EM, and stochastic approximation. but as the problem gets larger, it gets very very slow, and gets trapped at local maxima at the boundary of the parameter space.
Article Estimating a probability mass function with unknown labels
Hi Richard Gill. This question also was my focus. Therefore, I decided to develop a new particle filter scheme. This could be called as "Adaptive Particle Filter", because de likelihood function is up-dated ate each iteration. The paper was published as a book chapter (H. F. Campos Velho, H. C. M. Furtado: "Adaptive particle filter for stable distribution", book entitled "Integral Methods in Science and Engineering". New York: Birkhäuser, 2011, v. , p. 47-57). A previous version is available: http://iopscience.iop.org/1742-6596/135/1/012073
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