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Biometrika Advance Access published online on January 24, 2009
Biometrika, doi:10.1093/biomet/asn054
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© 2009 Biometrika Trust

Articles

Bayesian nonparametric functional data analysis through density estimation

Abel Rodríguez

Department of Applied Mathematics and Statistics, University of California, Mailstop SOE2, Santa Cruz, California 95064, U.S.A. abel{at}soe.ucsc.edu

David B. Dunson and Alan E. Gelfand

Department of Statistical Sciences, Box 90251, Duke University, Durham, North Carolina 27708, U.S.A. dunson{at}stat.duke.edu alan{at}isds.duke.edu

Received for publication 1 March 2007. Revision received 1 March 2008.
  Abstract

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.

Key Words: Dependent Dirichlet process • Functional clustering • Nonparametric Bayes inference • Nonparametric regression • Random probability measure


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