mixture

In probability and statistics, the term mixture is used for a joint probability distribution, a probability distribution resulting from one distribution applied to the results of another. For example, a source produces photons at random according to some distribution and a sensor detects the photons according to some other random distribution, so the resulting recorded data adheres to a distribution that is the result of both these. Mathematically, the mixture is a convolution of the two underlying distributions. Determining the underlying functions of such a convolution (deconvolution) is often of interest, but is not straight-forward, typically involving some kind of search, which can require much computation. Two approaches to efficient searching/checking are Markov chain Monte Carlo (MCMC) and mixture density networks (MDNs).

A mixture model is a model of some physical process that treats it as such a mixture distribution. Mixtures are typical in the way Bayesian statistics are currently used, and the term Bayesian mixture model is common.

The word mixture obviously has other unrelated scientific uses, such as within chemistry, materials mixed together but not forming a compound.