International Biometric Society Combinatorial Mixtures of Multiparameter Distributions: an Application to Bivariate Data

Combinatorial mixtures refers to a flexible class of models for inference on mixture distribu-tions [4] whose components have multidimensional parameters. The idea behind it is to al-low each element of component-specific parameter vectors to be shared by a subset of other components. We develop Bayesian inference and computation approaches for this class of distributions. We define a general prior distribution structure where a positive probability is put on every possible combination of sharing patterns, whence the name combinatorial mixtures. This partial sharing allows for greater generality and flexibility in comparison with traditional approaches to mixture modeling, while still allowing to assign significant mass to models that are more parsimonious than the general mixture case in which no sharing takes place. We illustrate our combinatorial mixtures in an application based on the normal model. We propose models for univariate and bivariate data. In the light of combinatorial mixtures, we adopt the decomposition of variance-covariance matrix proposed by Barnard et al. (2000) [1]. It separates the standard deviations and correlations, thus allowing to model those parameters separately. We develop a customized strategy to sample the correlation coefficient for each group. This work was originally motivated by the analysis of cancer subtypes: in terms of bio