Approximate Bayesian inference for simple mixtures
Keith Humphreys, D. Michael Titterington · COMPSTAT · 2000
Exact likelihoods and posterior densities associated with mixture data are computationally complex because of the large number of terms involved, corresponding to the large number of possible ways in which the observations might have evolved from the different components of the mixture. This feature is partially responsible for the need to use an algorithm such as the EM algorithm for calculating maximum likelihood estimates and, in Bayesian analysis, to represent posterior densities by a set of simulated samples generated by Markov chain Monte Carlo; see for instance Diebolt and Robert (1994).