A Bayesian approach to function alignment is introduced. A model is proposed in the ambient space, with a Dirichlet prior for the derivative of the warping function and a Gaussian process for the square root velocity function. Posterior inference is carried out via Markov chain Monte Carlo simulation. The methodology is applied to a dataset of mass spectrometry scans. Good alignment is obtained for most of the known proteins, with more uncertainty at either end of each scan.
"Analysis of proteomics data: Bayesian alignment of functions." Electron. J. Statist. 8 (2) 1734 - 1741, 2014. https://doi.org/10.1214/14-EJS900C