We present a Bayesian model for pairwise nonlinear registration of functional
data. We use the Riemannian geometry of the space of warping functions to
define appropriate prior distributions and sample from the posterior using
importance sampling. A simple square-root transformation is used to simplify
the geometry of the space of warping functions, which allows for computation of
sample statistics, such as the mean and median, and a fast implementation of a
k-means clustering algorithm. These tools allow for efficient posterior
inference, where multiple modes of the posterior distribution corresponding to
multiple plausible alignments of the given functions are found. We also show
pointwise 95% credible intervals to assess the uncertainty of the alignment
in different clusters. We validate this model using simulations and present
multiple examples on real data from different application domains including
biometrics and medicine