Alejandro Murua – Full Professor, Department of Mathematics and Statistics, Université de Montréal, Canada
Meeting ID: 992 4124 0063
We consider Bayesian nonparametric regression and survival 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 specific cases of Cox regression, and multivariate multiple regression, including sparse Bayesian neural networks.
This work has been done in collaboration with Fernando Quintana, Pontificia Universidad Catolica de Chile, and my students, Danae Martinez-Vargas and Karl-Augustt Alahassa.