Editing Mixture model (section)

{{Short description|Statistical concept}}
{{distinguish|mixed model}}
{{See also|Mixture distribution}}
In [[statistics]], a '''mixture model''' is a [[probabilistic model]] for representing the presence of [[subpopulation]]s within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the [[mixture distribution]] that represents the [[probability distribution]] of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make [[statistical inference]]s about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. Mixture models are used for clustering, under the name [[model-based clustering]], and also for [[density estimation]].

Mixture models should not be confused with models for [[compositional data]], i.e., data whose components are constrained to sum to a constant value (1, 100%, etc.). However, compositional models can be thought of as mixture models, where members of the population are sampled at random. Conversely, mixture models can be thought of as compositional models, where the [[measure (mathematics)|total size]] reading population has been normalized to 1.