Gibbs ensembles for nearly compatible and incompatible conditional models

Authors:
Shyh-Huei Chen;Edward H. Ip;Yuchung J. Wang
Affiliations:
Department of Industrial Management, National Yunlin University of Science and Technology, Douliu, Yunlin 640, Taiwan;Department of Biostatistical Sciences, Wake Forest University School of Medicine, Winston-Salem, NC 27157, USA;Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

The 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-using the Gibbs ensemble-is proposed for searching 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 relating to geno-polymorphism and response to chemotherapy for patients with metastatic colorectal cancer.