Semiparametric Bayesian Regression via Potts Model

• Published in: Journal of computational and graphical statistics Vol. 26; no. 2; pp. 265 - 274
• Main Authors: Murua, Alejandro, Quintana, Fernando A.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2017; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Bayesian Models; Clustering; Clusters; Health; Inference; Information; Mathematical models; Multivariate multiple linear regression; Nations; Partitions (mathematics); Predictions; Proximity; Random partition models; Regression; Regression analysis; Studies
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2016.1172015

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.