Mixture models

Imagine we are on an island taking measurements of lizard tail lengths. Not being carefully trained herpetologists, we do not realize that there are two species of lizard on the island. To our untrained eye, all of the lizards look to be of the same species. The distribution of tail lengths, then, might very well be bimodal, being separated by the species. But any one measurement could be from either species. Especially long tails might more likely be from species A and especially short trails may be more likely from species B, but tails of intermediate length could come from either. To model such a case, we use mixture models. In this section, we explore mixture models through an example of gene expression in different cell types. In so doing, we will also explore some more aspects of sampling and modeling with Stan.

Later, in 39  EM applied to a Gaussian mixture model, we will explore a class of models known as Gaussian mixture models, or GMMs.