Bayesian hierarchical curve registration

Functional data often exhibit a common shape, but with variations in amplitude and phase across curves. The analysis often proceeds by synchronization of the data through curve registration. In this article we propose a Bayesian hierarchical model for curve registration. Our hierarchical model provides a formal account of amplitude and phase variability while borrowing strength from the data across curves in the estimation of the model parameters. We discuss extensions of the model by using penalized B-splines in the representation of the shape and time-transformation functions, and by allowing temporal misalignment of the curves. We discuss applications of our model to simulated data, as well as to two data sets. In particular, we use our model in a nonstandard analysis aimed at investigating regulatory network in time course microarray data.