Mixture models assume that the data is multi-modal and drawn from a linear combination of uni-modal distributions. The expectation–maximization (EM) algorithm is a type of iterative unsupervised learning algorithm which alternates between updating the probability density of the state variables, based on model parameters (E-step) and updating the parameters by maximum likelihood estimation (M-step).The EM algorithm automatically determines the modality of the distribution and hence the number of components.A mixture model is only appropriate for use in finance if the modeler specifies which component is the most relevant for each observation.

Chapter 3 Bayesian Regression and Gaussian Processes