NONPARAMETRIC BAYES KERNEL-BASED PRIORS FOR FUNCTIONAL DATA ANALYSIS
Richard F. MacLehose, David B. Dunson · 2009
Abstract: 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 Dirich-let process for the weights. Theoretical properties are considered and an efficient MCMC algorithm is developed, relying on stick-breaking truncations. The meth-ods are illustrated using simulation examples and an application to reproductive hormone data.