Semiparametric Bayesian Regression via Potts Model
提出一种基于Potts聚类模型的协变量依赖先验分布，用于贝叶斯非参数回归，通过协变量邻近性驱动聚类形成和预测，在多元线性回归中表现良好，并应用于21世纪初各国健康状况分析。
We consider Bayesian nonparametric regression through random partition models. Our approach involves the construction of a covariate-dependent prior distribution on partitions of individuals. Our goal is to use covariate information to improve predictive inference. To do so, we propose a prior on partitions based on the Potts clustering model associated with the observed covariates. This drives by covariate proximity both the formation of clusters, and the prior predictive distribution. The resulting prior model is flexible enough to support many different types of likelihood models. We focus the discussion on nonparametric regression. Implementation details are discussed for the specific case of multivariate multiple linear regression. The proposed model performs well in terms of model fitting and prediction when compared to other alternative nonparametric regression approaches. We illustrate the methodology with an application to the health status of nations at the turn of the 21st century. Supplementary materials are available online.