Bayesian nonparametric functional data analysis through density estimation

• Published in: Biometrika
• Main Authors: Rodríguez, Abel, Dunson, David B., Gelfand, Alan E.
• Format: Text
• Language: English
• Published: Oxford University Press 2009
• Subjects: Articles; North Atlantic
• Online Access: http://biomet.oxfordjournals.org/cgi/content/short/asn054v1; https://doi.org/10.1093/biomet/asn054

In many modern experimental settings, observations are obtained in the form of functions and interest focuses on inferences about a collection of such functions. We propose a hierarchical model that allows us simultaneously to estimate multiple curves nonparametrically by using dependent Dirichlet process mixtures of Gaussian distributions to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the outcome given the predictors. The resulting approach allows for flexible estimation and clustering, while borrowing information across curves. We also show that the function estimates we obtain are consistent on the space of integrable functions. As an illustration, we consider an application to the analysis of conductivity and temperature at depth data in the north Atlantic.