Gibbs Ensembles for Nearly Compatible and Incompatible Conditional Models.

Gibbs sampler has been used exclusively for compatible conditionals that converge to a unique invariant joint distribution. However, conditional models are not always compatible. In this paper, a Gibbs sampling-based approach - Gibbs ensemble -is proposed to search for a joint distribution that deviates least from a prescribed set of conditional distributions. The algorithm can be easily scalable such that it can handle large data sets of high dimensionality. Using simulated data, we show that the proposed approach provides joint distributions that are less discrepant from the incompatible conditionals than those obtained by other methods discussed in the literature. The ensemble approach is also applied to a data set regarding geno-polymorphism and response to chemotherapy in patients with metastatic colorectal.