Semiparametric classification in hierarchical functional data analysis

Motivated by the problem of classifying hormone trajectories, this article proposes a flexible semiparametric Bayesian methodology for hierarchical functional data. The approach is based on a hierarchical spline model, with the number and location of knots and the distribution of the random spline coefficients treated as unknown. Assuming a discrete distribution for the spline coefficients, we obtain a procedure that clusters trajectories into classes, with the class-specific trajectories, the number of classes, and the allocation of subjects to classes unknown. This is accomplished through a generalization of the Dirichlet process to a collection of unknown distributions having varying dimension. An efficient reversible jump Markov chain Monte Carlo algorithm is developed by constructing dependency within this collection of distributions. The methods are illustrated using progesterone data.