Editing Mixture model (section)

== Extensions ==
In a [[Bayesian inference|Bayesian setting]], additional levels can be added to the [[graphical model]] defining the mixture model.  For example, in the common [[latent Dirichlet allocation]] [[topic model]], the observations are sets of words drawn from ''D'' different documents and the ''K'' mixture components represent topics that are shared across documents.  Each document has a different set of mixture weights, which specify the topics prevalent in that document.  All sets of mixture weights share common [[Hyperparameter (Bayesian statistics)|hyperparameter]]s.

A very common extension is to connect the [[latent variable]]s defining the mixture component identities into a [[Markov chain]], instead of assuming that they are [[independent identically distributed]] random variables.  The resulting model is termed a [[hidden Markov model]] and is one of the most common sequential hierarchical models.  Numerous extensions of hidden Markov models have been developed; see the resulting article for more information.