Gibbs Ensembles for Nearly Compatible and Incompatible Conditional Models
王友鐘 教授Rutgers University, USA 下午 2:00–2:50 鴻經館 107 室Gibbs sampler has been used exclusively for compatible conditionals that converge to a unique invariant joint distribution. However, conditional models are rarely compatible. In this talk, 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. It is also adaptive to different performance measures. Using simulated data, we show that the proposed approach provides joint distributions that are less discrepant from the incompatible conditionals than those obtained via linear programming and by pure Gibbs sampler. I will explain the central idea of ensemble and discuss its potentially wide applications in statistics. The ensemble approach is applied to a data set regarding geno-polymorphism and response to chemotherapy in patients with metastatic colorectal cancer. Its advantage in selecting conditional models will be illustrated.