Data integrative Bayesian inference for mixtures of regression models

Modern data collection techniques, which often produce different types of relevant information, call for new statistical learning methods that are adapted to cope with data integration. In the paper Bayesian inference is considered for mixtures of regression models with an unknown number of components, that facilitates data integration and variable selection for high dimensional data. In the approach presented, named data integrative mixture of regressions, data integration is accomplished by introducing a new data allocation scheme that summarizes additional data in the form of an informative prior on latent variables. To cope with high dimensionality, a shrinkage-type prior is assumed on the regression parameters, and a posteriori variable selection is conducted based on Bayesian credible intervals. Posterior estimation is achieved via a Markov chain Monte Carlo algorithm. The method is validated through simulation studies and illustrated by its performance on real data.