Bayesian nonparametric functional data analysis through density estimation
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 p...
| Published in: | Biometrika |
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| Main Authors: | , , |
| Format: | Text |
| Language: | English |
| Published: |
Oxford University Press
2009
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| Subjects: | |
| Online Access: | http://biomet.oxfordjournals.org/cgi/content/short/96/1/149 https://doi.org/10.1093/biomet/asn054 |
| Summary: | 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. |
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