March, 2007
In many modern experimental settings, observations are obtained in the
form of functions, and interest lays on inferences on a collection such
functions. Some examples are conductivity-temperature-depth (CTD)
data in oceanography, dose-response models in epidemiology and
time-course microarray experiments in biology an 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. 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 CTD data in the north
Atlantic.
Keywords: Nonparametric regressions; Consistency; Functional clustering; Dependent Dirichlet process; Nonparametric Bayes; Random probability measure.
The manuscript is available in PDF format.