Combinatorial mixtures of multiparameter distributions

Combinatorial mixtures refers to a flexible class of models for inference on mixture distributions whose components have multidimensional parameters. The approach is to allow each element of component-specific parameter vectors to be shared by a subset of other components. This allows for mixtures that range from very flexible to very parsimonious, and unifies the inference on component-specific parameters with that on the number of components. We develop Bayesian inference and computation approaches for this class of distributions, and illustrate them in an application based on the normal model. This work was originally motivated by the analysis of cancer subtypes: in terms of biological measures of interest, subtypes may be characterized by differences in location, scale, correlations or any of the combinations. We illustrate our approach in a simplified setting, using data on molecular subtypes of lung cancer.