NONPARAMETRIC FUNCTIONAL DATA ANALYSIS THROUGH BAYESIAN DENSITY ESTIMATION
In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivity-temperature-depth (CTD) data in oceanography, dose-response models in epidemiology and time-course microarray...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Text |
| Language: | English |
| Published: |
2007
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| Subjects: | |
| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.2506 http://ftp.isds.duke.edu/WorkingPapers/07-07.pdf |
| Summary: | In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivity-temperature-depth (CTD) data in oceanography, dose-response models in epidemiology and time-course microarray experiments in biology and medicine. In this paper we propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent Dirichlet Process mixtures of Gaussians to characterize the joint distribution of predictors and outcomes. Func-tion estimates are then induced through the conditional distribution of the outcome given the predic-tors. 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 inte-grable functions. As an illustration, we consider an application to the analysis of CTD data in the north Atlantic. |
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