Savitsky Terrance, Vannucci Marina
Department of Statistics, Rice University, Houston, TX 77030, USA ; Statistics group, RAND Corporation, Santa Monica, CA 90407, USA.
J Probab Stat. 2010;2010:201489. doi: 10.1155/2010/201489.
We expand a framework for Bayesian variable selection for Gaussian process (GP) models by employing spiked Dirichlet process (DP) prior constructions over set partitions containing covariates. Our approach results in a nonparametric treatment of the distribution of the covariance parameters of the GP covariance matrix that in turn induces a clustering of the covariates. We evaluate two prior constructions: the first one employs a mixture of a point-mass and a continuous distribution as the centering distribution for the DP prior, therefore, clustering all covariates. The second one employs a mixture of a spike and a DP prior with a continuous distribution as the centering distribution, which induces clustering of the selected covariates only. DP models borrow information across covariates through model-based clustering. Our simulation results, in particular, show a reduction in posterior sampling variability and, in turn, enhanced prediction performances. In our model formulations, we accomplish posterior inference by employing novel combinations and extensions of existing algorithms for inference with DP prior models and compare performances under the two prior constructions.
我们通过对包含协变量的集合划分采用尖峰狄利克雷过程（DP）先验构造，扩展了高斯过程（GP）模型的贝叶斯变量选择框架。我们的方法对GP协方差矩阵的协方差参数分布进行了非参数处理，进而导致协变量的聚类。我们评估了两种先验构造：第一种使用点质量分布和连续分布的混合作为DP先验的中心分布，从而对所有协变量进行聚类。第二种使用尖峰和具有连续分布的DP先验的混合作为中心分布，这仅会导致所选协变量的聚类。DP模型通过基于模型的聚类在协变量之间借用信息。特别是，我们的模拟结果表明后验采样变异性有所降低，进而提高了预测性能。在我们的模型公式中，我们通过采用用于DP先验模型推理的现有算法的新颖组合和扩展来完成后验推断，并比较两种先验构造下的性能表现。
