Editing Mixture model (section)

=== Markov chain Monte Carlo ===
As an alternative to the EM algorithm, the mixture model parameters can be deduced using [[posterior sampling]] as indicated by [[Bayes' theorem]].  This is still regarded as an incomplete data problem in which membership of data points is the missing data.  A two-step iterative procedure known as [[Gibbs sampling]] can be used.

The previous example of a mixture of two [[Gaussian distribution]]s can demonstrate how the method works.  As before, initial guesses of the parameters for the mixture model are made.  Instead of computing partial memberships for each elemental distribution, a membership value for each data point is drawn from a [[Bernoulli distribution]] (that is, it will be assigned to either the first or the second Gaussian).  The Bernoulli parameter ''θ'' is determined for each data point on the basis of one of the constituent distributions.{{Vague|What does this mean?|date=March 2008}}  Draws from the distribution generate membership associations for each data point.  Plug-in estimators can then be used as in the M step of EM to generate a new set of mixture model parameters, and the binomial draw step repeated.