Functional data often exhibit a common shape but also variations in amplitude and phase across curves. The analysis often proceed by synchronization of the data through curve registration. In this paper 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 utilizing penalized B–splines in the representation of the shape and time–transformation functions, and by allowing random image sets in the time transformation. We discuss applications of our model to simulated data as well as to two data sets. In particular, we illustrate using our model in a non–standard analysis aimed at investigating regulatory network in time course microarray data.
Keywords: Bayesian Hierarchical Model, Self–Modeling Regression, Curve Registration, Splines, Markov Chain Monte Carlo (MCMC), Time Course Microarray Experiments.