Kernel local partition processes for functional data

Functional data analysis commonly relies on the incorporation of basis functions having subject-specific coefficients, with the choice of basis and random effects distribution important. To allow the random effects distribution to be unknown, while inducing subject-specific basis selection and local borrowing of information across subjects, this article proposes a kernel local partition process (KLPP) prior. The KLPP selects the elements in a subject’s random effects vector locally from a collection of unique coefficient vectors, leading to a flexible local generalization of the Dirichlet process and to a sparse representation of complex functional data. Basic theoretical properties are considered, an MCMC algorithm is developed for posterior computation and the methods are applied to hormone data.