Nonparametric Bayes Kernel-Based Priors for Functional Data Analysis

We focus on developing nonparametric Bayes methods for collections of dependent random functions, allowing individual curves to vary flexibly while adaptively borrowing information. A prior is proposed, which is expressed as a hierarchical mixture of weighted kernels placed at unknown locations. The induced prior for any individual function is shown to fall within a reproducing kernel Hilbert space. We allow flexible borrowing of information through the use of a hierarchical Dirichlet process prior for the random locations, along with a functional Dirichlet process for the weights. Theoretical properties are considered and an efficient MCMC algorithm is developed, relying on stick-breaking truncations. The methods are illustrated using simulation examples and an application to reproductive hormone data.