Curve registration in functional data analysis

Functional data arise in numerous areas nowadays. When the functional responses evolve with respect to time, the subjects may experience events at different paces with the consequence that the sample curves are not aligned in some sense. An analysis as simple as estimation of the mean function without alignment will fail to produce a satisfactory estimator. Curve registration is one method in functional data analysis that attempts to solve this problem. A common registration method is landmark registration, which synchronizes the landmarks such as peaks or valleys. This approach can fail when the markers cannot be identified or are simply missing from some of the sample curves. Another common registration method is continuous monotone registration, which aims to align curves according to some target function. This works well but will fail if the target function is not chosen appropriately.; In this dissertation, a new model for registration is developed from a Bayesian perspective. It incorporates nonparametric spline curve fitting methods with continuous Monte Carlo Markov chain (MCMC) techniques. The functional response curves are fit by nonparametric spline methods with their coefficients treated as random parameters. Similarly, the warping functions are modeled as random spline functions and random shift and amplitude coefficients are also included in the model formulation. An MCMC algorithm is created to estimate the parameters in the model. The performance of the proposed method is evaluated in an empirical study.